Mixed metal dodecaborides and uses thereof

ABSTRACT

Disclosed herein, in certain embodiments, are compounds, methods, tools, and abrasive materials comprising mixed transition metal dodecaborides.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application No. 62/554,376, filed Sep. 5, 2017, which application is incorporated herein by reference.

STATEMENT AS TO FEDERALLY SPONSORED RESEARCH

This invention was made with Government support under Grant DMR-1506860 and Fellowship DGE-0654431, both awarded by the National Science Foundation. The Government has certain rights in the invention.

BACKGROUND OF THE INVENTION

In many manufacturing processes, materials must be cut, formed, or drilled and their surfaces protected with wear-resistant coatings. Diamond has traditionally been the material of choice for these applications, due to its superior mechanical properties, e.g. hardness >70 GPa. However, diamond is rare in nature and difficult to synthesize artificially due to the need for a combination of high temperature and high pressure conditions. Industrial applications of diamond are thus generally limited by cost. Moreover, diamond is not a good option for high-speed cutting of ferrous alloys due to its graphitization on the material's surface and formation of brittle carbides, which leads to poor cutting performance.

SUMMARY OF THE INVENTION

Disclosed herein, in certain embodiments, are composite materials, methods, tools, and abrasive materials comprising mixed metal dodecaborides.

In one embodiment is a composite matrix comprising:

-   -   Zr_(1-x)M_(x)B₁₂, or Y_(1-x)Sc_(x)B₁₂;         wherein:     -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),         neodymium (Nd), or praseodymium (Pr);     -   x is from 0.001 to 0.999.

In one embodiment, is a composite matrix comprising:

-   -   A_(1-x)M_(x)B_(c);         wherein:     -   A is zirconium (Zr), yttrium (Y) or scandium (Sc);     -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),         neodymium (Nd), praseodymium (Pr), terbium (Tb), dysprosium         (Dy), holmium (Ho), erbium (Er), thulium (Tm), ytterbium (Yb),         or lutetium (Lu);     -   x is from 0.001 to 0.999; and     -   c is 12-20; wherein     -   if A is Zr and c is 12, M is not Y, Sc, Gd, Sm, Nd, or Pr;     -   if A is Y and c is 12, M is not Sc;     -   if A is Sc and c is 12, M is not Y; and     -   A is not M.

In one embodiment, is a method of preparing a composite matrix described herein, wherein any of Zr, Y, Sc, Gd, Sm, or Nd and B are homogenized in an agate mortar and pestle or a vortex mixer, pressed under an 8-12 ton load, and arc melted under an argon atmosphere. In one embodiment, is a method of preparing a composite matrix described herein, wherein any of Zr, Y, Sc, Gd, Sm, Nd, Pr, Tb, Dy, Ho, Er, Tm, Yb, or Lu and B are homogenized in an agate mortar and pestle or a vortex mixer, pressed under an 8-12 ton load, and arc melted under an argon atmosphere.

In one embodiment, is a lightweight coating comprising a composite described herein.

In one embodiment, is a tool comprising a surface or body for cutting or abrading, wherein the surface or body comprises a composite matrix described herein.

INCORPORATION BY REFERENCE

All publications, patents, and patent applications mentioned in this specification are herein incorporated by reference to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated to be incorporated by reference.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

Various aspects of the invention are set forth with particularity in the appended claims. A better understanding of the features and advantages of the present invention will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the invention are utilized, and the accompanying drawings of which:

FIG. 1 shows X-ray powder diffractograms of Zr_(1-x)Y_(x)B₁₂.

FIG. 2 shows X-ray powder diffractograms of Zr_(1-x)Sc_(x)B₁₂.

FIG. 3 shows X-ray powder diffractograms of Y_(1-x)Sc_(x)B₁₂.

FIG. 4 shows X-ray powder diffractograms of Zr_(1-x)Gd_(x)B₁₂.

FIG. 5 shows X-ray powder diffractograms of Zr_(1-x)Sm_(x)B₁₂.

FIG. 6 shows X-ray powder diffractograms of Zr_(1-x)Nd_(x)B₁₂.

FIG. 7 shows X-ray powder diffractograms of Zr_(1-x)Pr_(x)B₁₂.

FIG. 8 shows measurements of Vickers microindentation hardness of Zr_(1-x)Y_(x)B₁₂.

FIG. 9 shows measurements of Vickers microindentation hardness of Zr_(1-x)Sc_(x)B₁₂.

FIG. 10 shows measurements of Vickers microindentation hardness of Y_(1-x)Sc_(x)B₁₂.

FIG. 11 shows measurements of Vickers microindentation hardness of Zr_(1-x)Gd_(x)B₁₂.

FIG. 12 shows the thermal stability of Zr_(0.5)Y_(0.5)B₁₂, Zr_(0.5)Sc_(0.5)B₁₂, and Y_(0.5)Sc_(0.5)B₁₂ as measured by thermal gravimetric analysis in air.

FIG. 13 shows the thermal stability of pure Zr_(0.5)Gd_(0.5)B₁₂ and Zr_(0.75)Sm_(0.25)B₁₂ as measured by thermal gravimetric analysis in air.

FIG. 14 shows the X-ray powder diffractograms of Zr_(1-x)Y_(x)B₁₂ prepared with a metal to boron ratio of 1:13.

FIG. 15 shows the unit cell of the cubic dodecaboride structure type, cubic-UB₁₂ polyhedra model, the unit cell of the tetragonal-ScB₁₂ dodecaboride structure type and the tetragonal-ScB₁₂ polyhedra model.

FIG. 16 shows the crystal structure of ScBso and the crystal structure of YB₆₆.

FIG. 17 shows a polyhedra model of the unit cell of a cubic-UB₁₂ structural type metal dodecaboride, a polyhedra model of the unit cell of a tetragonal-ScB₁₂ structural type metal dodecaboride, a polyhedra model of the unit cell of a rhombohedral-MB₅₀ structural type metal boride, and a polyhedra model of the unit cell of a cubic-YB₆₆ structural type metal boride.

FIG. 18 shows elemental maps and SEM images of selected samples of Zr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Nd_(x)B₁₂ and Zr_(1-x)Pr_(x)B₁₂ alloys.

FIG. 19 shows the SEM images and elemental maps for the hardest compositions of the mixed metal dodecaborides: Zr_(0.5)Y_(0.5)B₁₂, Zr0.5Sc_(0.5)B₁₂ and Y0.5Sc_(0.5)B₁₂.

FIG. 20 shows the colors of solid solution samples of the mixed metal dodecaborides Zr_(1-x)Y_(x)B₁₂, Zr_(1-x)Sc_(x)B₁₂, and Y_(1-x)Sc_(x)B₁₂ taken using an optical microscope.

FIG. 21 shows the colors of solid solution samples of the mixed metal dodecaborides Zr_(1-x)Gd_(x)B₁₂, and Zr_(1-x)Sm_(x)B₁₂, taken using an optical microscope.

FIG. 22 shows a transmission electron microscopy image of Zr_(0.05)Sc_(0.95)B₁₂.

FIG. 23 shows the tetragonal diffraction pattern of Zr0.05Sc_(0.95)B₁₂.

FIG. 24 shows powder XRD patterns of ScB₅₀ and YB₆₆.

DETAILED DESCRIPTION OF THE INVENTION

Wear and tear are part of the normal use of tools and machines. There are different types of wear mechanisms, including, for example, abrasion wear, adhesion wear, attrition wear, diffusion wear, fatigue wear, edge chipping (or premature wear), and oxidation wear (or corrosive wear). Abrasion wear occurs when the hard particle or debris, such as chips, passes over or abrades the surface of a cutting tool. Adhesion wear or attrition wear occurs when debris removes microscopic fragments from a tool. Diffusion wear occurs when atoms in a crystal lattice move from a region of high concentration to a region of low concentration and the move weakens the surface structure of a tool. Fatigue wear occurs at a microscopic level when two surfaces slide in contact with each other under high pressure, generating surface cracks. Edge chipping or premature wear occurs as small breaking away of materials from the surface of a tool. Oxidation wear or corrosive wear occurs as a result of a chemical reaction between the surface of a tool and oxygen.

The present application discloses new materials having enhanced resistance to the above-mentioned types of wear and tear. The development of new materials with superior mechanical properties is challenging because of the many attributes that need to be controlled, ranging from hardness to oxidation resistance. These new material formulations may need to be superhard (defined as having Vickers hardness (Hv) greater than 40 GPa at a given force of applied load), so that they may be able to supplant tungsten carbide (Hv=13-25 GPa at 0.5 N of applied loading, force comparable to that experienced by materials during cutting and machining), the current industrial standard for drilling and machining, as well as having similar or superior oxidation resistance.

Indeed, the discovery of new superhard materials in higher borides comes from attempts to simulate diamond, the hardest material known thus far. Diamond is both highly incompressible and resistant to shear; together, this accounts for diamond's superior resistance to surface deformation and thus, high hardness. Not surprisingly, there are few compounds that possess the requisite attributes for superhardness, and among them are the higher metal borides. For ReB₂, CrB₄ and WB₄, the high electron density of the transition metal provides the ultra-incompressibility, while the high density of covalent bonds prevents the propagation of slip.

Metal dodecaborides (MB₁₂) constitute a class of boron rich compounds previously studied for their magnetic, optical and electronic properties. The structure of all dodecaborides contains boron cuboctahedron cages composed of 24 atoms, each containing a 12-coordinate metal in its center. The cages are usually arranged in a face-centered cubic close packed arrangement, forming the cubic-UB₁₂ Fm3m structure; however, ScB₁₂ forms its own structural type—tetragonal—ScBl2 (I4/mmm), where the cuboctahedra are arranged in a body-centered tetragonal close-packed structure. Dodecaborides are known to exist for a number of metals: transition metals (Zr, Hf, Y and Sc), lanthanides (Tb, Dy, Ho, Er, Tm, Yb and Lu) and actinides (U and Th). For the most part, the aforementioned dodecaborides have been prepared via arc melting from the elements, or by borothermal reduction of the metal oxide under vacuum, to yield fully dense ingots or compacts, respectively. HfB₁₂ and ThB₁₂ are especially interesting, since in pure form they can only be formed under high pressure (6.5 GPa) and high temperature (1660° C.); however, they can be stabilized under ambient pressure in the matrices of ZrB₁₂ (Zr_(1-x)Th_(x)B₁₂) and YB₁₂ (Y_(1-x)Hf_(x)B₁₂).

The size of a metal atom in a 12-coordinate environment places limitations on which atoms can fit inside a boron cuboctahedral environment and form a metal dodecaboride. All metal dodecaborides, stable under ambient pressure, have metal atoms with sizes intermediate between zirconium (r_(at)=1.55 Å, r_(CN=12)=1.603 Å) and yttrium (r_(at)=1.80 Å, r_(CN=12)=1.801 Å), the smallest and largest metal atoms, respectively, capable of forming a stable transition metal dodecaboride. Therefore, this size requirement results in the stable dodecaboride lattice parameter lying between 7.408 Å (ZrB₁₂) and 7.500 Å (YB₁₂).

Dodecaborides where the metal cation lies outside the range of stability (HfB₁₂, GdB₁₂ and ThB₁₂) requires pressures upwards of 6.5 GPa. These phases have metal atoms either smaller than zirconium (Hf, r_(at)=1.55 Å, r_(CN=12)=1.580 Å) and thus incapable of accommodating the boron cuboctahedron cage, or larger that yttrium, resulting in a unit cell far exceeding the size of the YB₁₂ cell (a=7.524 Å for GdB₁₂ and a=7.612 Å for ThB₁₂). The broad applicability of high-pressure synthesis for dodecaborides of all sizes comes from differences in incompressibility between the metal atom and the boron network. For HfB₁₂, hafnium is more incompressible than the boron network; thus, the boron network shrinks in size under applied pressure, increasing the effective size of the hafnium atom. For GdB₁₂ and ThB₁₂ the effect is reversed, with the effective size of the metal atom shrinking due to the increased compressibility of gadolinium and thorium atoms when compared to the boron network.

Described herein is the stabilization of the high-pressure phase of GdB₁₂ in a matrix of ZrB₁₂, with a solubility of Gd in ZrB₁₂ reaching 54 at. % Gd, along with select properties. Also described are the stabilizations with limited solubilities (below 15%) of previously un-synthesized SmB₁₂, NdB₁₂ and PrB₁₂ in ZrB₁₂ matrices, demonstrating a decrease in solubility with increasing size of the secondary metal.

Pure dodecaborides are superhard, which can be attributed to their high isotropy and stiff metal-boron bonds as well as boron-boron bonds forming the cuboctahedra. MB₁₂, as secondary phases, are also known to increase the hardness of other borides, such as WB4, through extrinsic hardening mechanisms. Atomic radii may play a determining role in the different structural types of tetragonal-ScB₁₂ and cubic-MB but electronic structure of the atoms also plays an important role. Scandium, although being a transition metal, behaves more like an alkaline-earth metal.

Apart from the fundamental interest of metal MB₁₂ due to their unique structure, their properties are also of interest in industrial applications, such as Zr-based cutting tools and abrasives (with abrasive qualities comparable to that of diamond, but producing less roughening of surfaces). Therefore, the mechanical properties (superhardness), lightweight (due to density comparable or lower than that of diamond (3.52 g/cm³)) and enhanced oxidation resistance properties are of interest for potential applications in machining industries and as lightweight protective coatings.

In some embodiments, described herein include composite matrix materials, when applied to a tool or abrasive material, reduce the rate of oxidation wear of the tool or abrasive material, or inhibit oxidation wear of the tool or abrasive material. In some embodiments, also described herein include methods of manufacturing of the composite matrix, and tools and abrasive materials for use with the composite matrix.

In one embodiment is a composite matrix comprising:

-   -   Zr_(1-x)M_(x)B₁₂, or Y_(1-x)Sc_(x)B₁₂;         wherein:     -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),         neodymium (Nd), or praseodymium (Pr);     -   x is from 0.001 to 0.999.

In some embodiments of a composite matrix described herein, x is 0.001-0.200. In some embodiments of a composite matrix described herein, x is 0.201-0.400. In some embodiments of a composite matrix described herein, x is 0.401-0.600. In some embodiments of a composite matrix described herein, x is 0.601-0.800. In some embodiments of a composite matrix described herein, x is 0.801-0.999. In some embodiments of a composite matrix described herein, x is 0.25. In some embodiments of a composite matrix described herein, x is 0.50. In some embodiments of a composite matrix described herein, x is 0.75. In some embodiments of a composite matrix described herein, x is 0.80. In some embodiments of a composite matrix described herein, x is 0.85. In some embodiments of a composite matrix described herein, x is 0.90. In some embodiments of a composite matrix described herein, x is 0.95. In some embodiments of a composite matrix described herein, the composite matrix is resistant to oxidation.

In some embodiments of a composite matrix described herein, the composite matrix is resistant to oxidation below 620° C. In some embodiments of a composite matrix described herein, the composite matrix is resistant to oxidation below 675° C. In some embodiments of a composite matrix described herein, the composite matrix is resistant to oxidation below 685° C.

In some embodiments of a composite matrix described herein, the composite matrix possesses a density of 4.0 g/cm³ or less. In some embodiments of a composite matrix described herein, the composite matrix possesses a density of 3.55 g/cm³ or less. In some embodiments of a composite matrix described herein, the composite matrix possesses a density of 3.35 g/cm³ or less.

In some embodiments of a composite matrix described herein, the composite matrix possesses a density of 3.21 g/cm³ or less. In some embodiments of a composite matrix described herein, the composite matrix possesses a hardness between 38.0 and 52.0 GPa. In some embodiments of a composite matrix described herein, the composite matrix possesses a hardness between 44.0 and 48.0 GPa. In some embodiments of a composite matrix described herein, the composite matrix possesses a hardness between 45.0 and 51.0 GPa. In some embodiments of a composite matrix described herein, the composite matrix possesses a hardness between 42.0 and 48.0 GPa. In some embodiments of a composite matrix described herein, the composite matrix possesses a hardness between 38.0 and 45.0 GPa.

In some embodiments of a composite matrix described herein, the composite matrix unit cell is cubic or tetragonal. In some embodiments of a composite matrix described herein, the composite matrix unit cell is cubic and the length of a is between 7.350 and 7.550 Å, wherein a is the length between two adjacent vertices in the unit cell. In some embodiments of a composite matrix described herein, the composite matrix unit cell is tetragonal and the length of a is between 5.150 and 5.450 Å, where a is the shortest length between two adjacent vertices in the unit cell, and the length of c is between 7.350 and 7.550 Å, where c is the longest length between two adjacent vertices in the unit cell.

In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂. In some embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂. In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂. In some embodiments, the composite matrix is Zr_(1-x)Gd_(x)B₁₂. In some embodiments, the composite matrix is Zr_(1-x)Sm_(x)B₁₂. In some embodiments, the composite matrix is Zr_(1-x)Nd_(x)B₁₂. In some embodiments, the composite matrix is Zr_(1-x)Pr_(x)B₁₂.

In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂ and characterized by X-ray diffraction pattern reflections given in Table 8. In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂ and characterized by at least one X-ray diffraction pattern reflection given in Table 8. In some embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ and characterized by X-ray diffraction pattern reflections given in Tables 9 or 10. In some embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ and characterized by at least one X-ray diffraction pattern reflection given in Table 9 or 10. In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and characterized by X-ray diffraction pattern reflections given in Table 11 or₁₂. In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and characterized by at least one X-ray diffraction pattern reflection given in Table 11 or 12. In some embodiments, the composite matrix is Zr_(1-x)Gd_(x)B₁₂ and characterized by X-ray diffraction pattern reflections given in Table 13. In some embodiments, the composite matrix is Zr_(1-x)Gd_(x)B₁₂ and characterized by at least one X-ray diffraction pattern reflection given in Table 13. In some embodiments, the composite matrix is Zr_(1-x)Sm_(x)B₁₂ and characterized by X-ray diffraction pattern reflections given in Table 14. In some embodiments, the composite matrix is Zr_(1-x)Sm_(x)B₁₂ and characterized by at least one X-ray diffraction pattern reflection given in Table 14. In some embodiments, the composite matrix is Zr_(1-x)Nd_(x)B₁₂ and characterized by X-ray diffraction pattern reflections given in Table 15. In some embodiments, the composite matrix is Zr_(1-x)Nd_(x)B₁₂ and characterized by at least one X-ray diffraction pattern reflection given in Table 15. In some embodiments, the composite matrix is Zr_(1-x)Pr_(x)B₁₂ and characterized by X-ray diffraction pattern reflections given in Table 16. In some embodiments, the composite matrix is Zr_(1-x)Pr_(x)B₁₂ and characterized by at least one X-ray diffraction pattern reflection given in Table 16.

In one embodiment is a composite matrix comprising:

-   -   A_(1-x)M_(x)B_(c);         wherein:     -   A is zirconium (Zr), yttrium (Y) or scandium (Sc);     -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),         neodymium (Nd), praseodymium (Pr), terbium (Tb), dysprosium         (Dy), holmium (Ho), erbium (Er), thulium (Tm), ytterbium (Yb),         or lutetium (Lu);     -   x is from 0.001 to 0.999; and     -   c is 12-20; wherein     -   if A is Zr and c is 12, M is not Y, Sc, Gd, Sm, Nd, or Pr;     -   if A is Y and c is 12, M is not Sc;     -   if A is Sc and c is 12, M is not Y; and     -   A is not M.

In another embodiment is a method of preparing a composite matrix described herein, wherein the raw materials are homogenized in an agate mortar and pestle or vortex mixer, pressed under an 8-12 ton load, and arc melted under an argon atmosphere. In another embodiment is a method of preparing a composite matrix described herein, wherein the arc melting is performed using a current of over 50 A for a time of between 0.01 and 5 minutes. In another embodiment is a method of preparing a composite matrix described herein, wherein the arc melting is performed using a current of over between 65-75 A for a time of between 1 and 2 minutes.

In another embodiment is a lightweight coating comprising a composite matrix described herein.

In another embodiment is a tool comprising a surface or body for cutting or abrading, wherein the surface or body comprises a composite matrix described herein.

In one embodiment is a composite matrix comprising:

-   -   Zr_(1-x)M_(x)B₁₂, or Y_(1-x)Sc_(x)B₁₂;         wherein:     -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),         neodymium (Nd), or praseodymium (Pr);     -   x is from 0.001 to 0.999.

In one embodiment, the composite matrix is resistant to oxidation. In one embodiment, the composite matrix possesses a density of 4.0 g/cm³ or less. In one embodiment, the composite matrix possesses a hardness between 38.0 and 52.0 GPa. In one embodiment, the composite matrix is crystalline. In one embodiment, the composite matrix is crystalline and comprises a unit cell that is cubic or tetragonal as determined by X-ray powder diffraction. In one embodiment, the unit cell is cubic and the length between two adjacent vertices in the unit cell is a, and a is from 7.350 to 7.550 Å. In one embodiment, the unit cell is tetragonal and comprises two distinct lengths between one vertex and at least two adjacent vertices, wherein the two distinct lengths comprise a first length c and a second length a, wherein c is from 7.350 to 7.550 Å and a is from 5.150 to 5.450 Å. In one embodiment, the composite matrix is Zr_(1-x)Y_(x)B₁₂. In one embodiment, the composite matrix is Zr_(1-x)Sc_(x)B₁₂. In one embodiment, the composite matrix is Yi,Sc_(x)B₁₂. In one embodiment, the composite matrix is Zr_(1-x)Gd_(x)B₁₂. In one embodiment, the composite matrix is Zr_(1-x)Sm_(x)B₁₂. In one embodiment, the composite matrix is Zr_(1-x)Nd_(x)B₁₂. In one embodiment, the composite matrix is Zr_(1-x)Pr_(x)B₁₂.

In one embodiment, is a composite matrix comprising:

-   -   A_(1-x)M_(x)B_(c);         wherein:     -   A is zirconium (Zr), yttrium (Y) or scandium (Sc);     -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),         neodymium (Nd), praseodymium (Pr), terbium (Tb), dysprosium         (Dy), holmium (Ho), erbium (Er), thulium (Tm), ytterbium (Yb),         or lutetium (Lu);     -   x is from 0.001 to 0.999; and     -   c is 12-20; wherein     -   if A is Zr and c is 12, M is not Y, Sc, Gd, Sm, Nd, or Pr;     -   if A is Y and c is 12, M is not Sc;     -   if A is Sc and c is 12, M is not Y; and     -   A is not M.

In one embodiment, the composite matrix is Y_(1-x)Gd_(x)B_(c), Sc_(1-x)Gd_(x)B_(c), Y_(1-x)Sm_(x)B_(c), Sc_(1-x)Sm_(x)B_(c), Y_(1-x)Nd_(x)B_(c), Sc_(1-x)Nd_(x)B_(c), Y_(1-x)Pr_(x)B_(c), Sc_(1-x)Pr_(x)B_(c), Zr_(1-x)Tb_(x)B_(c), Y_(1-x)Tb_(x)B_(c), Sc_(1-x)Tb_(x)B_(c), Zr_(1-x)Dy_(x)B_(c), Y_(1-x)DY_(x)B_(c), Sc_(1-x)Dy_(x)B_(c), Zr_(1-x)Ho_(x)B_(c), Y_(1-x)Ho_(x)B_(c), Sc_(1-x)Ho_(x)B_(c), Zr_(1-x)Er_(x)B_(c), Y_(1-x)Er_(x)B_(c), Sc_(1-x)Er_(x)B_(c), Zr_(1-x)Tm_(x)B_(c), Y_(1-x)Tm_(x)B_(c), Sc_(1-x)Tm_(x)B_(c), Zr_(1-x)Yb_(x)B_(c), Y_(1-x)Yb_(x)B_(c), Sc_(1-x)Yb_(x)B_(c), Zr_(1-x)Lu_(x)B_(c), Y_(1-x)Lu_(x)B_(c), or Sc_(1-x)Lu_(x)B_(c). In one embodiment, is a method of preparing a composite matrix described herein, wherein any of Zr, Y, Sc, Gd, Sm, or Nd and B are homogenized in an agate mortar and pestle or a vortex mixer, pressed under an 8-12 ton load, and arc melted under an argon atmosphere. In one embodiment, is a method of preparing a composite matrix described herein, wherein any of Zr, Y, Sc, Gd, Sm, Nd, Pr, Tb, Dy, Ho, Er, Tm, Yb, or Lu and B are homogenized in an agate mortar and pestle or a vortex mixer, pressed under an 8-12 ton load, and arc melted under an argon atmosphere.

In one embodiment, is a lightweight coating comprising a composite described herein.

In one embodiment, is a tool comprising a surface or body for cutting or abrading, wherein the surface or body comprises a composite matrix described herein.

Mixed Metal Dodecaboride Composite Matrix

In some embodiments, a composite matrix described herein comprises a composition comprising at least two metals and boron (B). In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms is about 1 to 12. In some embodiments, the composite matrix is a superhard material. In some embodiments, the composite matrix comprises a solid solution phase. In some embodiments, the composite matrix is resistant to oxidation.

In some embodiments, a composite matrix described herein comprises a composition comprising at least two metals and boron (B). In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms is from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In one embodiment, described herein is a composite matrix comprising:

-   -   Zr_(1-x)M_(x)B₁₂, or Y_(1-x)Sc_(x)B₁₂;         wherein:     -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),         neodymium (Nd), or praseodymium (Pr);     -   x is from 0.001 to 0.999.

In some embodiments, M is Y. In some embodiments, M is Sc. In some embodiments, M is Gd. In some embodiments, M is Sm. In some embodiments, M is Nd. In some embodiments, M is Pr.

In some embodiments, M comprises Y, Sc, Gd, Sm, Nd, or Pr. In some embodiments, M comprises Y or Sc. In some embodiments, M comprises Gd, Sm, Nd, or Pr.

In some embodiments, M comprises at least Y. In some embodiments, M comprises at least Sc. In some embodiments, M comprises at least Gd. In some embodiments, M comprises at least Sm. In some embodiments, M comprises at least Nd. In some embodiments, M comprises at least Pr. In some embodiments, M comprises two or more elements selected from Y, Sc, Gd, Sm, Nd, or Pr.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Y_(x)B_(c);         wherein:     -   x is from 0.001 to 0.999; and     -   c is 12-20.

In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B_(c) and prepared with a ratio of all metal atoms to boron atoms from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Y_(x)B₁₂;         wherein:     -   x is from 0.001 to 0.999.

In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂ and prepared with a ratio of all metal atoms to boron atoms from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Sc_(1-x)B_(c);         wherein:     -   x is from 0.001 to 0.999; and     -   c is 12-20.

In some embodiments, the composite matrix is Zr_(1-x)Sc_(1-x)B_(c) and prepared with a ratio of all metal atoms to boron atoms from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Sc_(x)B₁₂;         wherein:     -   x is from 0.001 to 0.999.

In some embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ and prepared with a ratio of all metal atoms to boron atoms from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Y_(1-x)Sc_(x)B_(c);         wherein:     -   x is from 0.001 to 0.999; and     -   c is 12-20.

In some embodiments, the composite matrix Y_(1-x)Sc_(1-x)B_(c) and prepared with a ratio of all metal atoms to boron atoms from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Y_(1-x)Sc_(x)B₁₂;         wherein:     -   x is from 0.001 to 0.999.

In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and prepared with a ratio of all metal atoms to boron atoms from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Gd_(x)B_(c);         wherein:     -   x is from 0.001 to 0.999; and     -   c is 12-20.

In some embodiments, the composite matrix is Zr_(1-x)Gd_(x)B_(c) and prepared with a ratio of all metal atoms to boron atoms from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Gd_(x)B₁₂;         wherein:     -   x is from 0.001 to 0.999.

In some embodiments, the composite matrix is Zr_(1-x)Gd_(x)B₁₂ and prepared with a ratio of all metal atoms to boron atoms from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Sm_(x)B_(c);         wherein:     -   x is from 0.001 to 0.999; and     -   c is 12-20.

In some embodiments, the composite matrix is Zr_(1-x)Sm_(x)B_(c) and prepared with a ratio of all metal atoms to boron atoms from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Sm_(x)B₁₂;         wherein:     -   x is from 0.001 to 0.999.

In some embodiments, the composite matrix is Zr_(1-x)Sm_(x)B₁₂ and prepared with a ratio of all metal atoms to boron atoms from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Nd_(x)B_(c);         wherein:     -   x is from 0.001 to 0.999; and     -   c is 12-20.

In some embodiments, the composite matrix Zr_(1-x)Nd_(x)B_(c) and prepared with a ratio of all metal atoms to boron atoms from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Nd_(x)B₁₂;         wherein:     -   x is from 0.001 to 0.999.

In some embodiments, the composite matrix is Zr_(1-x)Nd_(x)B₁₂ and prepared with a ratio of all metal atoms to boron atoms from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Pr_(x)B_(c);         wherein:     -   x is from 0.001 to 0.999; and     -   c is 12-20.

In some embodiments, the composite matrix is Zr_(1-x)Pr_(x)B_(c) and prepared with a ratio of all metal atoms to boron atoms from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Pr_(x)B₂;         wherein:     -   x is from 0.001 to 0.999.

In some embodiments, the composite matrix is Zr_(1-x)Pr_(x)B₁₂ and prepared with a ratio of all metal atoms to boron atoms from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In one embodiment is a composite matrix comprising:

-   -   A_(1-x)M_(x)B_(c);         wherein:     -   A is zirconium (Zr), yttrium (Y) or scandium (Sc);     -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),         neodymium (Nd), praseodymium (Pr), terbium (Tb), dysprosium         (Dy), holmium (Ho), erbium (Er), thulium (Tm), ytterbium (Yb),         or lutetium (Lu);     -   x is from 0.001 to 0.999; and     -   c is 12-20; wherein     -   if A is Zr and c is 12, M is not Y, Sc, Gd, Sm, Nd, or Pr;     -   if A is Y and c is 12, M is not Sc;     -   if A is Sc and c is 12, M is not Y; and     -   A is not M.

In some embodiments, the composite matrix is resistant to oxidation.

In some embodiments, the composite matrix is Y_(1-x)Gd_(x)B_(c), Sc_(1-x)Gd_(x)B_(c), Y_(1-x)Sm_(x)B_(c), Sc_(1-x)Sm_(x)B_(c), Y_(1-x)Nd_(x)B_(c), Sc_(1-x)Nd_(x)B_(c), Y_(1-x)Pr_(x)B_(c), Sc_(1-x)Pr_(x)B_(c), Zr_(1-x)Tb_(x)B_(c), Y_(1-x)Tb_(x)B_(c), Sc_(1-x)Tb_(x)B_(c), Zr_(1-x)Dy_(x)B_(c), Y_(1-x)DY_(x)B_(c), Sc_(1-x)DY_(x)B_(c), Zr_(1-x)Ho_(x)B_(c), Y_(1-x)Ho_(x)B_(c), Sc_(1-x)Ho_(x)B_(c), Zr_(1-x)Er_(x)B_(c), Y_(1-x)Er_(x)B_(c), Sc_(1-x)Er_(x)B_(c), Zr_(1-x)Tm_(x)B_(c), Y_(1-x)Tm_(x)B_(c), Sc_(1-x)Tm_(x)B_(c), Zr_(1-x)Yb_(x)B_(c), Y_(1-x)Yb_(x)B_(c), Sc_(1-x)Yb_(x)B_(c), Zr_(1-x)Lu_(x)B_(c), Y_(1-x)Lu_(x)B_(c), or Sc_(1-x)Lu_(x)B_(c).

In some embodiments, the composite matrix is Y_(1-x)Gd_(x)B₁₂, Sc_(1-x)Gd_(x)B₁₂, Y_(1-x)Sm_(x)B₁₂, Sc_(1-x)Sm_(x)B₁₂, Y_(1-x)Nd_(x)B₁₂, Sc_(1-x)Nd_(x)B₁₂, Y_(1-x)Pr_(x)B₁₂, Sc_(1-x)Pr_(x)B₁₂, Zr_(1-x)Tb_(x)B₁₂, Y_(1-x)Tb_(x)B₁₂, Sc_(1-x)Tb_(x)B₁₂, Zr_(1-x)Dy_(x)B₁₂, Y_(1-x)Dy_(x)B₁₂, Sc_(1-x)Dy_(x)B₁₂, Zr_(1-x)Ho_(x)B₁₂, Y_(1-x)Ho_(x)B₁₂, Sc_(1-x)Ho_(x)B₁₂, Zr_(1-x)Er_(x)B₁₂, Y_(1-x)Er_(x)B₁₂, Sc_(1-x)Er_(x)B₁₂, Zr_(1-x)Tm_(x)B₁₂, Y_(1-x)Tm_(x)B₁₂, Sc_(1-x)Tm_(x)B₁₂, Zr_(1-x)Yb_(x)B₁₂, Y_(1-x)Yb_(x)B₁₂, Sc_(1-x)Yb_(x)B₁₂, Zr_(1-x)Lu_(x)B₁₂, Y_(1-x)Lu_(x)B₁₂, or Sc_(1-x)Lu_(x)B₁₂.

In some embodiments, the composite matrix is A_(1-x)M_(x)B_(c) and prepared with a ratio of all metal atoms to boron atoms from about 1 to 12 to about 1 to 20. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 12. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 13. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 14. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 15. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 16. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 17. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 18. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 19. In some embodiments, the composite matrix is prepared with a ratio of all metal atoms to boron atoms of about 1 to 20.

In some embodiments, x has a value within the range 0.001 to 0.999, inclusively. In some embodiments, x has a value within the range 0.005 to 0.99, 0.01 to 0.95, 0.05 to 0.9, 0.1 to 0.9, 0.001 to 0.6, 0.005 to 0.6, 0.01 to 0.6, 0.05 to 0.6, 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, 0.4 to 0.6, 0.001 to 0.55, 0.005 to 0.55, 0.01 to 0.55, 0.05 to 0.55, 0.1 to 0.55, 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, 0.45 to 0.55, 0.001 to 0.5, 0.005 to 0.5, 0.01 to 0.5, 0.05 to 0.5, 0.1 to 0.5, 0.2 to 0.5, 0.3 to 0.5, 0.4 to 0.5, 0.5 to 0.55, 0.45 to 0.5, 0.001 to 0.4, 0.005 to 0.4, 0.01 to 0.4, 0.05 to 0.4, 0.1 to 0.4, 0.2 to 0.4, 0.001 to 0.3, 0.005 to 0.3, 0.01 to 0.3, 0.05 to 0.3, 0.1 to 0.3, 0.001 to 0.2, 0.005 to 0.2, 0.01 to 0.2, 0.05 to 0.2, or 0.1 to 0.2, inclusively. In some embodiments, x has a value within the range 0.1 to 0.9, inclusively. In some embodiments, x has a value within the range 0.001 to 0.6, 0.005 to 0.6, 0.001 to 0.4, or 0.001 to 0.2, inclusively. In some embodiments, x has a value within the range 0.001 to 0.6, inclusively. In some embodiments, x has a value within the range 0.001 to 0.5, inclusively. In some embodiments, x has a value within the range 0.001 to 0.4, inclusively. In some embodiments, x has a value within the range 0.001 to 0.3, inclusively. In some embodiments, x has a value within the range 0.001 to 0.2, inclusively. In some embodiments, x has a value within the range 0.01 to 0.6, inclusively. In some embodiments, x has a value within the range 0.01 to 0.5, inclusively. In some embodiments, x has a value within the range 0.01 to 0.4, inclusively. In some embodiments, x has a value within the range 0.01 to 0.3, inclusively. In some embodiments, x has a value within the range 0.01 to 0.2, inclusively. In some embodiments, x has a value within the range 0.1 to 0.8, inclusively. In some embodiments, x has a value within the range 0.1 to 0.7, inclusively. In some embodiments, x has a value within the range 0.1 to 0.6, inclusively. In some embodiments, x has a value within the range 0.1 to 0.5, inclusively. In some embodiments, x has a value within the range 0.1 to 0.4, inclusively. In some embodiments, x has a value within the range 0.1 to 0.3, inclusively. In some embodiments, x has a value within the range 0.1 to 0.2, inclusively. In some embodiments, x has a value within the range 0.2 to 0.8, inclusively. In some embodiments, x has a value within the range 0.2 to 0.7, inclusively. In some embodiments, x has a value within the range 0.2 to 0.6, inclusively. In some embodiments, x has a value within the range 0.2 to 0.5, inclusively. In some embodiments, x has a value within the range 0.2 to 0.4, inclusively. In some embodiments, x has a value within the range 0.2 to 0.3, inclusively. In some embodiments, x has a value within the range 0.3 to 0.8, inclusively. In some embodiments, x has a value within the range 0.3 to 0.7, inclusively. In some embodiments, x has a value within the range 0.3 to 0.6, inclusively. In some embodiments, x has a value within the range 0.3 to 0.5, inclusively. In some embodiments, x has a value within the range 0.3 to 0.4, inclusively. In some embodiments, x has a value within the range 0.4 to 0.8, inclusively. In some embodiments, x has a value within the range 0.4 to 0.7, inclusively. In some embodiments, x has a value within the range 0.4 to 0.6, inclusively. In some embodiments, x has a value within the range 0.4 to 0.5, inclusively.

In some embodiments, x is at least 0.001 and less than 0.999. In some embodiments, x is at least 0.001 and less than 0.9. In some embodiments, x is at least 0.001 and less than 0.6. In some embodiments, x is at least 0.001 and less than 0.5. In some embodiments, x is at least 0.001 and less than 0.4. In some embodiments, x is at least 0.001 and less than 0.3. In some embodiments, x is at least 0.001 and less than 0.2. In some embodiments, x is at least 0.001 and less than 0.05. In some embodiments, x is at least 0.01 and less than 0.5. In some embodiments, x is at least 0.01 and less than 0.4. In some embodiments, x is at least 0.01 and less than 0.3. In some embodiments, x is at least 0.01 and less than 0.2. In some embodiments, x is at least 0.1 and less than 0.5. In some embodiments, x is at least 0.1 and less than 0.4. In some embodiments, x is at least 0.1 and less than 0.3. In some embodiments, xis at least 0.1 and less than 0.2.

In some embodiments, x has a value of about 0.001, 0.005, 0.01, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.65, 0.7, 0.8, 0.9, 0.95, 0.99, or about 0.999. In some embodiments, x has a value of about 0.001. In some embodiments, x has a value of about 0.005. In some embodiments, x has a value of about 0.01. In some embodiments, x has a value of about 0.05. In some embodiments, x has a value of about 0.1. In some embodiments, x has a value of about 0.15. In some embodiments, x has a value of about 0.2. In some embodiments, x has a value of about 0.3. In some embodiments, x has a value of about 0.4. In some embodiments, x has a value of about 0.41. In some embodiments, x has a value of about 0.42. In some embodiments, x has a value of about 0.43. In some embodiments, x has a value of about 0.44. In some embodiments, x has a value of about 0.45. In some embodiments, x has a value of about 0.46. In some embodiments, x has a value of about 0.47. In some embodiments, x has a value of about 0.48. In some embodiments, x has a value of about 0.49. In some embodiments, x has a value of about 0.5. In some embodiments, x has a value of about 0.51. In some embodiments, x has a value of about 0.52. In some embodiments, x has a value of about 0.53. In some embodiments, x has a value of about 0.54. In some embodiments, x has a value of about 0.55. In some embodiments, x has a value of about 0.56. In some embodiments, x has a value of about 0.57. In some embodiments, x has a value of about 0.58. In some embodiments, x has a value of about 0.59. In some embodiments, x has a value of about 0.6. In some embodiments, x has a value of about 0.7. In some embodiments, x has a value of about 0.8. In some embodiments, x has a value of about 0.9. In some embodiments, x has a value of about 0.99.

In some embodiments, x is 0.001-0.200. In some embodiments, x is 0.201-0.400. In some embodiments, x is 0.401-0.600. In some embodiments, x is 0.601-0.800. In some embodiments, x is 0.801-0.999.

In some embodiments, x is about 0.05. In some embodiments, x is about 0.25. In some embodiments, x is about 0.50. In some embodiments, x is about 0.75. In some embodiments, x is about 0.80. In some embodiments, x is about 0.85. In some embodiments, x is about 0.90. In some embodiments, x is about 0.95.

In some embodiments, c has a value of 12-20. In some embodiments, c has a value of 12. In some embodiments, c has a value of 13. In some embodiments, c has a value of 14. In some embodiments, c has a value of 15. In some embodiments, c has a value of 16. In some embodiments, c has a value of 17. In some embodiments, c has a value of 18. In some embodiments, c has a value of 19. In some embodiments, c has a value of 20. In some embodiments, c has a value within the range of 12-13. In some embodiments, c has a value within the range of 13-14. In some embodiments, c has a value within the range of 14-15. In some embodiments, c has a value within the range of 15-16. In some embodiments, c has a value within the range of 17-18. In some embodiments, c has a value within the range of 19-20. In some embodiments, c has a value within the range of 12-14. In some embodiments, c has a value within the range of 12-16. In some embodiments, c has a value within the range of 12-18. In some embodiments, c has a value within the range of 14-16. In some embodiments, c has a value within the range of 14-18.In some embodiments, c has a value within the range of 14-20. In some embodiments, c has a value within the range of 16-18. In some embodiments, c has a value within the range of 16-20. In some embodiments, c has a value within the range of 18-20.

In some embodiments M is Y, and x is at least 0.001 and less than 0.999. In some embodiments M is Y, and x is at least 0.100 and less than 0.900. In some embodiments M is Y, and x is at least 0.200 and less than 0.800. In some embodiments M is Y, and x is at least 0.300 and less than 0.700. In some embodiments M is Y, and x is at least 0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Y_(0.05)B₁₂. In some embodiments, the composite matrix is Zr_(0.90)Y_(0.10)B₁₂. In some embodiments, the composite matrix is Zr_(0.85)Y_(0.15)B₁₂. In some embodiments, the composite matrix is Zr_(0.80)Y_(0.20)B₁₂. In some embodiments, the composite matrix is Zr_(0.75)Y_(0.25)B₁₂. In some embodiments, the composite matrix is Zr_(0.70)Y_(0.30)B₁₂. In some embodiments, the composite matrix is Zr_(0.65)Y_(0.35)B₁₂. In some embodiments, the composite matrix is Zr_(0.60)Y_(0.40)B₁₂. In some embodiments, the composite matrix is Zr_(0.55)Y_(0.45)B₁₂. In some embodiments, the composite matrix is Zr_(0.50)Y_(0.50)B₁₂. In some embodiments, the composite matrix is Zr_(0.45)Y_(0.55)B₁₂. In some embodiments, the composite matrix is Zr_(0.40)Y_(0.60)B₁₂. In some embodiments, the composite matrix is Zr_(0.35)Y_(0.65)B₁₂. In some embodiments, the composite matrix is Zr_(0.30)Y_(0.70)B₁₂. In some embodiments, the composite matrix is Zr_(0.25)Y_(0.75)B₁₂. In some embodiments, the composite matrix is Zr_(0.20)Y_(0.65)B₁₂. In some embodiments, the composite matrix is Zr_(0.15)Y_(0.85)B₁₂. In some embodiments, the composite matrix is Zr_(0.10)Y_(0.90)B₁₂. In some embodiments, the composite matrix is Zr_(0.05)Y_(0.95)B₁₂.

In some embodiments M is Sc, and x is at least 0.001 and less than 0.999. In some embodiments M is Sc, and x is at least 0.100 and less than 0.900. In some embodiments M is Sc, and x is at least 0.200 and less than 0.800. In some embodiments M is Sc, and x is at least 0.300 and less than 0.700. In some embodiments M is Sc, and x is at least 0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Sc_(0.05)B₁₂. In some embodiments, the composite matrix is Zr_(0.90) SC 0.10B₁₂. In some embodiments, the composite matrix is Zr_(0.85)Sc_(0.15)B₁₂. In some embodiments, the composite matrix is Zr_(0.80)Sc_(0.20)B₁₂. In some embodiments, the composite matrix is Zr_(0.75)Sc_(0.25)B₁₂. In some embodiments, the composite matrix is Zr_(0.70)Sc_(0.30)B₁₂. In some embodiments, the composite matrix is Zr_(0.65)Sc_(0.35)B₁₂. In some embodiments, the composite matrix is Zr_(0.60)Sc_(0.40)B₁₂. In some embodiments, the composite matrix is Zr_(0.70)Sc_(0.45)B₁₂. In some embodiments, the composite matrix is Zr_(0.50)Sc_(0.50)B₁₂. In some embodiments, the composite matrix is Zr_(0.45)Sc_(0.55)B₁₂. In some embodiments, the composite matrix is Zr_(0.40)Sc_(0.60)B₁₂. In some embodiments, the composite matrix is Zr_(0.35)Sc_(0.65)B₁₂. In some embodiments, the composite matrix is Zr_(0.30)Sc_(0.70)B₁₂. In some embodiments, the composite matrix is Zr_(0.25)Sc_(0.75)B₁₂. In some embodiments, the composite matrix is Zr_(0.20)Sc_(0.80)B₁₂. In some embodiments, the composite matrix is Zr_(0.15)Sc_(0.85)B₁₂. In some embodiments, the composite matrix is Zr_(0.10)Sc 0.90B₁₂. In some embodiments, the composite matrix is Zro.os Sc 0.95B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Sc_(0.05)B₁₂. In some embodiments, the composite matrix is Y_(0.90)Sc_(0.10)B₁₂. In some embodiments, the composite matrix is Y_(0.85)Sc_(0.15)B₁₂. In some embodiments, the composite matrix is Y_(0.80)Sc_(0.20)B₁₂. In some embodiments, the composite matrix is Y_(0.75)Sc_(0.25)B₁₂. In some embodiments, the composite matrix is Y_(0.70)Sc_(0.30)B₁₂. In some embodiments, the composite matrix is Y_(0.65)Sc_(0.35)B₁₂. In some embodiments, the composite matrix is Y_(0.60)Sc_(0.40)B₁₂. In some embodiments, the composite matrix is Y_(0.55)Sc_(0.45)B₁₂. In some embodiments, the composite matrix is Y_(0.50)Sc_(0.50)B₁₂. In some embodiments, the composite matrix is Y_(0.45)Sc_(0.55)B₁₂. In some embodiments, the composite matrix is Y_(0.40)Sc_(0.60)B₁₂. In some embodiments, the composite matrix is Y_(0.35)Sc_(0.65)B₁₂. In some embodiments, the composite matrix is Y_(0.30)Sc_(0.70)B₁₂. In some embodiments, the composite matrix is Y_(0.25)Sc_(0.75)B₁₂. In some embodiments, the composite matrix is Y_(0.20)Sc_(0.80)B₁₂. In some embodiments, the composite matrix is Y_(0.15)Sc_(0.85)B₁₂. In some embodiments, the composite matrix is Y_(0.10)Sc_(0.90)B₁₂. In some embodiments, the composite matrix is Y_(0.05)Sc_(0.95)B₁₂.

In some embodiments M is Gd, and x is at least 0.001 and less than 0.999. In some embodiments M is Gd, and x is at least 0.100 and less than 0.900. In some embodiments M is Gd, and x is at least 0.200 and less than 0.800. In some embodiments M is Gd, and x is at least 0.300 and less than 0.700. In some embodiments M is Gd, and x is at least 0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Gd_(0.05)B₁₂. In some embodiments, the composite matrix is Zr_(0.90)Gd_(0.10)B₁₂. In some embodiments, the composite matrix is Zr_(0.85)Gd_(0.15)B₁₂. In some embodiments, the composite matrix is Zr_(0.80)Gd_(0.20)B₁₂. In some embodiments, the composite matrix is Zr_(0.75)Gd_(0.25)B₁₂. In some embodiments, the composite matrix is Zr_(0.70)Gd_(0.30)B₁₂. In some embodiments, the composite matrix is Zr_(0.65) Gd_(0.35)B₁₂. In some embodiments, the composite matrix is Zr_(0.60)Gd_(0.40)B₁₂. In some embodiments, the composite matrix is Zr_(0.55)Gd_(0.45)B₁₂. In some embodiments, the composite matrix is Zr_(0.50)Gd_(0.50)B₁₂. In some embodiments, the composite matrix is Zr_(0.45)Gd_(0.55)B₁₂. In some embodiments, the composite matrix is Zr_(0.40)Gd_(0.60)B₁₂. In some embodiments, the composite matrix is Zr_(0.35) Gd_(0.65)B₁₂. In some embodiments, the composite matrix is Zr_(0.30)Gd_(0.70)B₁₂. In some embodiments, the composite matrix is Zr_(0.25) Gd_(0.75)B₁₂. In some embodiments, the composite matrix is Zr_(0.20)Gd_(0.80)B₁₂. In some embodiments, the composite matrix is Zr_(0.15)Gd_(0.0312). In some embodiments, the composite matrix is Zr_(0.10)Gd_(0.90)B₁₂. In some embodiments, the composite matrix is Zr_(0.05)Gd_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Gd_(0.05)B₁₂. In some embodiments, the composite matrix is Y_(0.90)Gd_(0.10)B₁₂. In some embodiments, the composite matrix is Y_(0.85)Gd_(0.15)B₁₂. In some embodiments, the composite matrix is Y_(0.80)Gd_(0.20)B₁₂. In some embodiments, the composite matrix is Y_(0.75)Gd_(0.25)B₁₂. In some embodiments, the composite matrix is Y_(0.70)Gd_(0.30)B₁₂. In some embodiments, the composite matrix is Y_(0.65) Gd_(0.35)B₁₂. In some embodiments, the composite matrix is Y_(0.60)Gd_(0.40)B₁₂. In some embodiments, the composite matrix is Y_(0.55)Gd_(0.45)B₁₂. In some embodiments, the composite matrix is Y_(0.50)Gd_(0.50)B₁₂. In some embodiments, the composite matrix is Y_(0.45)Gd_(0.55)B₁₂. In some embodiments, the composite matrix is Y_(0.40)Gd_(0.60)B₁₂. In some embodiments, the composite matrix is Y_(0.35)Gd_(0.65)B₁₂. In some embodiments, the composite matrix is Y_(0.30)Gd_(0.70)B₁₂. In some embodiments, the composite matrix is Y_(0.25)Gd_(0.75)B₁₂. In some embodiments, the composite matrix is Y_(0.20)Gd_(0.0312). In some embodiments, the composite matrix is Y_(0.15)Gd_(0.85)B₁₂. In some embodiments, the composite matrix is Y_(0.10)Gd_(0.90)B₁₂. In some embodiments, the composite matrix is Y_(0.05)Gd_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Gd_(0.05)B₁₂. In some embodiments, the composite matrix is Sc_(0.90)Gd_(0.10)B₁₂. In some embodiments, the composite matrix is Sc_(0.85)Gd_(0.15)B₁₂. In some embodiments, the composite matrix is Sc_(0.80)Gd_(0.20)B₁₂. In some embodiments, the composite matrix is Sc_(0.75)Gd_(0.25)B₁₂. In some embodiments, the composite matrix is Sc_(0.70)Gd_(0.30)B₁₂. In some embodiments, the composite matrix is Sc_(0.65) Gd_(0.35)B₁₂. In some embodiments, the composite matrix is Sc_(0.60)Gd_(0.40)B₁₂. In some embodiments, the composite matrix is Sc_(0.55)Gd_(0.45)B₁₂. In some embodiments, the composite matrix is Sc_(0.50)Gd_(0.50)B₁₂. In some embodiments, the composite matrix is Sc_(0.45)Gd_(0.55)B₁₂. In some embodiments, the composite matrix is Sc_(0.40)Gd_(0.60)B₁₂. In some embodiments, the composite matrix is Sc_(0.35) Gd_(0.65)B₁₂. In some embodiments, the composite matrix is Sc_(0.30)Gd_(0.70)B₁₂. In some embodiments, the composite matrix is Sc_(0.25)Gd_(0.75)B₁₂. In some embodiments, the composite matrix is Sc_(0.20)Gd_(0.80)B₁₂. In some embodiments, the composite matrix is Sc_(0.15)Gd_(0.0312). In some embodiments, the composite matrix is Sc_(0.10)Gd_(0.90)B₁₂. In some embodiments, the composite matrix is Sc_(0.05)Gd_(0.95)B₁₂.

In some embodiments M is Sm, and x is at least 0.001 and less than 0.999. In some embodiments M is Sm, and x is at least 0.100 and less than 0.900. In some embodiments M is Sm, and x is at least 0.200 and less than 0.800. In some embodiments M is Sm, and x is at least 0.300 and less than 0.700. In some embodiments M is Sm, and x is at least 0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Sm_(0.05)B₁₂. In some embodiments, the composite matrix is Zr_(0.90)Sm_(0.10)B₁₂. In some embodiments, the composite matrix is Zr_(0.85)Sm_(0.15)B₁₂. In some embodiments, the composite matrix is Zr_(0.80)Sm_(0.20)B₁₂. In some embodiments, the composite matrix is Zr_(0.75)Sm_(0.25)B₁₂. In some embodiments, the composite matrix is Zr_(0.70)Sm_(0.30)B₁₂. In some embodiments, the composite matrix is Zr_(0.65)Sm_(0.35)B₁₂. In some embodiments, the composite matrix is Zr_(0.60)Sm_(0.40)B₁₂. In some embodiments, the composite matrix is Zr_(0.55)Sm_(0.45)B₁₂. In some embodiments, the composite matrix is Zr_(0.50)Sm_(0.50)B₁₂. In some embodiments, the composite matrix is Zr_(0.45)Sm_(0.55)B₁₂. In some embodiments, the composite matrix is Zr_(0.40)Sm_(0.60)B₁₂. In some embodiments, the composite matrix is Zr_(0.35)Sm_(0.65)B₁₂. In some embodiments, the composite matrix is Zr_(0.30)Sm_(0.70)B₁₂. In some embodiments, the composite matrix is Zr_(0.25)Sm_(0.75)B₁₂. In some embodiments, the composite matrix is Zr_(0.20)Sm_(0.80)B₁₂. In some embodiments, the composite matrix is Zr_(0.15)Sm_(0.85)B₁₂. In some embodiments, the composite matrix is Zr_(0.10)Sm_(0.90)B₁₂. In some embodiments, the composite matrix is Zr_(0.05)Sm_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Sm_(0.05)B₁₂. In some embodiments, the composite matrix is Y_(0.90)Sm_(0.10)B₁₂. In some embodiments, the composite matrix is Y_(0.85)Sm_(0.15)B₁₂. In some embodiments, the composite matrix is Y_(0.80)Sm_(0.20)B₁₂. In some embodiments, the composite matrix is Y_(0.75)Sm_(0.25)B₁₂. In some embodiments, the composite matrix is Y_(0.70)Sm_(0.30)B₁₂. In some embodiments, the composite matrix is Y_(0.65)Sm_(0.35)B₁₂. In some embodiments, the composite matrix is Y_(0.60)Sm_(0.40)B₁₂. In some embodiments, the composite matrix is Y_(0.55)Sm_(0.45)B₁₂. In some embodiments, the composite matrix is Y_(0.50)Sm_(0.50)B₁₂. In some embodiments, the composite matrix is Y_(0.45)Sm_(0.55)B₁₂. In some embodiments, the composite matrix is Y_(0.40)Sm_(0.60)B₁₂. In some embodiments, the composite matrix is Y_(0.35)Sm_(0.65)B₁₂. In some embodiments, the composite matrix is Y_(0.30)Sm_(0.70)B₁₂. In some embodiments, the composite matrix is Y_(0.25)Sm_(0.75)B₁₂. In some embodiments, the composite matrix is Y_(0.20)Sm_(0.80)B₁₂. In some embodiments, the composite matrix is Y_(0.15)Sm_(0.85)B₁₂. In some embodiments, the composite matrix is Y_(0.10)Sm_(0.90)B₁₂. In some embodiments, the composite matrix is Y_(0.05)Sm_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Sm_(0.05)B₁₂. In some embodiments, the composite matrix is Sc_(0.90)Sm_(0.10)B₁₂. In some embodiments, the composite matrix is Sc_(0.85)Sm_(0.15)B₁₂. In some embodiments, the composite matrix is Sc_(0.80)Sm_(0.20)B₁₂. In some embodiments, the composite matrix is Sc_(0.75)Sm_(0.25)B₁₂. In some embodiments, the composite matrix is Sc_(0.70)Sm_(0.30)B₁₂. In some embodiments, the composite matrix is Sc_(0.65)Sm_(0.35)B₁₂. In some embodiments, the composite matrix is Sc_(0.60)Sm_(0.40)B₁₂. In some embodiments, the composite matrix is Sc_(0.55)Sm_(0.45)B₁₂. In some embodiments, the composite matrix is Sc_(0.50)Sm_(0.50)B₁₂. In some embodiments, the composite matrix is Sc_(0.45)Sm_(0.55)B₁₂. In some embodiments, the composite matrix is Sc_(0.40)Sm_(0.60)B₁₂. In some embodiments, the composite matrix is Sc_(0.35)Sm_(0.65)B₁₂. In some embodiments, the composite matrix is Sc_(0.30)Sm_(0.70)B₁₂. In some embodiments, the composite matrix is Sc_(0.25)Sm_(0.75)B₁₂. In some embodiments, the composite matrix is Sc_(0.20)Sm_(0.80)B₁₂. In some embodiments, the composite matrix is Sc_(0.15)Sm_(0.85)B₁₂. In some embodiments, the composite matrix is Sc_(0.10)Sm_(0.90)B₁₂. In some embodiments, the composite matrix is Sc_(0.05)Sm_(0.95)B₁₂.

In some embodiments M is Nd, and x is at least 0.001 and less than 0.999. In some embodiments M is Nd, and x is at least 0.100 and less than 0.900. In some embodiments M is Nd, and x is at least 0.200 and less than 0.800. In some embodiments M is Nd, and x is at least 0.300 and less than 0.700. In some embodiments M is Nd, and x is at least 0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Nd_(0.05)B₁₂. In some embodiments, the composite matrix is Zr_(0.90)Nd_(0.10)B₁₂. In some embodiments, the composite matrix is Zr_(0.85)Nd_(0.15)B₁₂. In some embodiments, the composite matrix is Zr_(0.80)Nd_(0.20)B₁₂. In some embodiments, the composite matrix is Zr_(0.75)Nd_(0.25)B₁₂. In some embodiments, the composite matrix is Zr_(0.70)Nd_(0.30)B₁₂. In some embodiments, the composite matrix is Zr_(0.65) Nd0.35B₁₂. In some embodiments, the composite matrix is Zr_(0.60)Nd_(0.40)B₁₂. In some embodiments, the composite matrix is Zr_(0.55) Nd_(0.45)B₁₂. In some embodiments, the composite matrix is Zr_(0.50)Nd_(0.50)B₁₂. In some embodiments, the composite matrix is Zr_(0.45) Nd_(0.55)B₁₂. In some embodiments, the composite matrix is Zr_(0.40) Nd_(0.60)B₁₂. In some embodiments, the composite matrix is Zr_(0.35) Nd0.65B₁₂. In some embodiments, the composite matrix is Zr_(0.30)Nd_(0.70)B₁₂. In some embodiments, the composite matrix is Zr_(0.25) Nd0.75B₁₂. In some embodiments, the composite matrix is Zr_(0.20)Nd_(0.80)B₁₂. In some embodiments, the composite matrix is Zr_(0.15) Nd_(0.85)B₁₂. In some embodiments, the composite matrix is Zrodo Nd_(0.90)B₁₂. In some embodiments, the composite matrix is Zr_(0.05) Nd_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Nd_(0.05)B₁₂. In some embodiments, the composite matrix is Y_(0.90)Nd_(0.10)B₁₂. In some embodiments, the composite matrix is Y_(0.85)Nd_(0.15)B₁₂. In some embodiments, the composite matrix is Y_(0.80)Nd_(0.20)B₁₂. In some embodiments, the composite matrix is Y_(0.75)Nd_(0.25)B₁₂. In some embodiments, the composite matrix is Y_(0.70)Nd_(0.30)B₁₂. In some embodiments, the composite matrix is Y_(0.65)Nd_(0.35)B₁₂. In some embodiments, the composite matrix is Y_(0.60)Nd_(0.40)B₁₂. In some embodiments, the composite matrix is Y_(0.55) Nd_(0.45)B₁₂. In some embodiments, the composite matrix is Y_(0.50)Nd_(0.50)B₁₂. In some embodiments, the composite matrix is Y_(0.45) Nd_(0.55)B₁₂. In some embodiments, the composite matrix is Y_(0.40) Nd_(0.60)B₁₂. In some embodiments, the composite matrix is Y_(0.35)Nd_(0.65)B₁₂. In some embodiments, the composite matrix is Y_(0.30) Nd_(0.70)B₁₂. In some embodiments, the composite matrix is Y_(0.25) Nd_(0.75)B₁₂. In some embodiments, the composite matrix is Y_(0.20)Nd_(0.0312). In some embodiments, the composite matrix is Y_(0.15) Nd_(0.85)B₁₂. In some embodiments, the composite matrix is Y_(0.10)Nd_(0.90)B₁₂. In some embodiments, the composite matrix is Y_(0.05)Nd_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Nd_(0.05)B₁₂. In some embodiments, the composite matrix is Sc_(0.90) Nd_(0.10)B₁₂. In some embodiments, the composite matrix is Sc_(0.85)Nd_(0.15)B₁₂. In some embodiments, the composite matrix is Sc_(0.80)Nd_(0.20)B₁₂. In some embodiments, the composite matrix is Sc_(0.75)Nd_(0.25)B₁₂. In some embodiments, the composite matrix is Sc_(0.70)Nd_(0.30)B₁₂. In some embodiments, the composite matrix is Sc_(0.65) Nd_(0.35)B₁₂. In some embodiments, the composite matrix is Sc_(0.60)Nd_(0.40)B₁₂. In some embodiments, the composite matrix is Sc_(0.55)Nd_(0.45)B₁₂. In some embodiments, the composite matrix is Sc_(0.50)Nd_(0.50)B₁₂. In some embodiments, the composite matrix is Sc_(0.45)Nd_(0.55)B₁₂. In some embodiments, the composite matrix is Sc_(0.40)Nd_(0.60)B₁₂. In some embodiments, the composite matrix is Sc_(0.35) Nd_(0.65)B₁₂. In some embodiments, the composite matrix is Sc_(0.30)Nd_(0.70)B₁₂. In some embodiments, the composite matrix is Sc_(0.25)Nd_(0.75)B₁₂. In some embodiments, the composite matrix is Sc_(0.20)Nd_(0.80)B₁₂. In some embodiments, the composite matrix is Sc_(0.15)Nd_(0.85)B₁₂. In some embodiments, the composite matrix is Sc_(0.10)Nd_(0.90)B₁₂. In some embodiments, the composite matrix is Sc_(0.05)Nd_(0.95)B₁₂.

In some embodiments M is Pr, and x is at least 0.001 and less than 0.999. In some embodiments M is Pr, and x is at least 0.100 and less than 0.900. In some embodiments M is Pr, and x is at least 0.200 and less than 0.800. In some embodiments M is Pr, and x is at least 0.300 and less than 0.700. In some embodiments M is Pr, and x is at least 0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Pr_(0.05)B₁₂. In some embodiments, the composite matrix is Zr_(0.90)Pr_(0.10)B₁₂. In some embodiments, the composite matrix is Zr_(0.85)Pr_(0.15)B₁₂. In some embodiments, the composite matrix is Zr_(0.80)Pr_(0.20)B₁₂. In some embodiments, the composite matrix is Zr_(0.75)Pr_(0.25)B₁₂. In some embodiments, the composite matrix is Zr_(0.70)Pr_(0.30)B₁₂. In some embodiments, the composite matrix is Zr_(0.65)Pr_(0.35)B₁₂. In some embodiments, the composite matrix is Zr_(0.60)Pr_(0.40)B₁₂. In some embodiments, the composite matrix is Zr_(0.55)Pr_(0.45)B₁₂. In some embodiments, the composite matrix is Zr_(0.50)Pr_(0.50)B₁₂. In some embodiments, the composite matrix is Zr_(0.45)Pr_(0.55)B₁₂. In some embodiments, the composite matrix is Zr_(0.40)Pr_(0.60)B₁₂. In some embodiments, the composite matrix is Zr_(0.35)Pr_(0.65)B₁₂. In some embodiments, the composite matrix is Zr_(0.30)Pr_(0.70)B₁₂. In some embodiments, the composite matrix is Zr_(0.25)Pr_(0.75)B₁₂. In some embodiments, the composite matrix is Zr_(0.20)Pr_(0.80)B₁₂. In some embodiments, the composite matrix is Zr_(0.15)Pr_(0.85)B₁₂. In some embodiments, the composite matrix is Zr_(0.10)Pr_(0.90)B₁₂. In some embodiments, the composite matrix is Zr_(0.05)Pr_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Pr_(0.05)B₁₂. In some embodiments, the composite matrix is Y_(0.90)Pr_(0.10)B₁₂. In some embodiments, the composite matrix is Y_(0.85)Pr_(0.15)B₁₂. In some embodiments, the composite matrix is Y_(0.80)Pr_(0.20)B₁₂. In some embodiments, the composite matrix is Y_(0.75)Pr_(0.25)B₁₂. In some embodiments, the composite matrix is Y_(0.70)Pr_(0.30)B₁₂. In some embodiments, the composite matrix is Y_(0.65)Pr_(0.35)B₁₂. In some embodiments, the composite matrix is Y_(0.60)Pr_(0.40)B₁₂. In some embodiments, the composite matrix is Y_(0.55)Pr_(0.45)B₁₂. In some embodiments, the composite matrix is Yo.so Pr_(0.50)B₁₂. In some embodiments, the composite matrix is Y_(0.45)Pr_(0.55)B₁₂. In some embodiments, the composite matrix is Y_(0.40)Pr_(0.60)B₁₂. In some embodiments, the composite matrix is Y_(0.35)Pr_(0.65)B₁₂. In some embodiments, the composite matrix is Y_(0.30)Pr_(0.70)B₁₂. In some embodiments, the composite matrix is Y_(0.25)Pr_(0.75)B₁₂. In some embodiments, the composite matrix is Y_(0.20)Pr_(0.80)B₁₂. In some embodiments, the composite matrix is Y_(0.15)Pr_(0.03)B₁₂. In some embodiments, the composite matrix is Y_(0.10)Pr_(0.90)B₁₂. In some embodiments, the composite matrix is

Y_(0.05)Pr_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Pr_(0.05)B₁₂. In some embodiments, the composite matrix is Sc_(0.90)Pr_(0.10)B₁₂. In some embodiments, the composite matrix is Sc_(0.85)Pr_(0.15)B₁₂. In some embodiments, the composite matrix is Sc_(0.80)Pr_(0.20)B₁₂. In some embodiments, the composite matrix is Sc_(0.75)Pr_(0.25)B₁₂. In some embodiments, the composite matrix is Sc_(0.70)Pr_(0.30)B₁₂. In some embodiments, the composite matrix is Sc_(0.65)Pr_(0.35)B₁₂. In some embodiments, the composite matrix is Sc_(0.60)Pr_(0.40)B₁₂. In some embodiments, the composite matrix is Sc_(0.55)Pr_(0.45)B₁₂. In some embodiments, the composite matrix is Sc_(0.50)Pr_(0.50)B₁₂. In some embodiments, the composite matrix is Sc_(0.45)Pr_(0.55)B₁₂. In some embodiments, the composite matrix is Sc_(0.40)Pr_(0.60)B₁₂. In some embodiments, the composite matrix is Sc_(0.35)Pr_(0.65)B₁₂. In some embodiments, the composite matrix is Sc_(0.30)Pr_(0.70)B₁₂. In some embodiments, the composite matrix is Sc_(0.25)Pr_(0.75)B₁₂. In some embodiments, the composite matrix is Sc_(0.20)Pr_(0.0312). In some embodiments, the composite matrix is Sc_(0.15)Pr_(0.85)B₁₂. In some embodiments, the composite matrix is Sc_(0.10)Pr_(0.90)B₁₂. In some embodiments, the composite matrix is Sc_(0.05)Pr_(0.95)B₁₂.

In some embodiments, the composite matrix is Zr_(1-x)Tb_(x)B₁₂, Y_(1-x)Tb_(x)B₁₂, Sc_(1-x)Tb_(x)B₁₂, Zr_(1-x)Dy_(x)B₁₂, Y_(1-x)Dy_(x)B₁₂, Sc_(1-x)Dy_(x)B₁₂, Zr_(1-x)Ho_(x)B₁₂, Y_(1-x)Ho_(x)B₁₂, Sc_(1-x)Ho_(x)B₁₂, Zr_(1-x)Er_(x)B₁₂, Y_(1-x)Er_(x)B₁₂, Sc_(1-x)Er_(x)B₁₂, Zr_(1-x)Tm_(x)B₁₂, Y_(1-x)Tm_(x)B₁₂, Sc_(1-x)Tm_(x)B₁₂, Zr_(1-x)Yb_(x)B₁₂, Y₁-xYb_(x)B₁₂, Sc_(1-x)Yb_(x)B₁₂, Zr_(1-x)Lu_(x)B₁₂, Y_(1-x)Lu_(x)B₁₂, or Sc_(1-x)Lu_(x)B₁₂.

In some embodiments M is Tb, and x is at least 0.001 and less than 0.999. In some embodiments M is Tb, and x is at least 0.100 and less than 0.900. In some embodiments M is Tb, and x is at least 0.200 and less than 0.800. In some embodiments M is Tb, and x is at least 0.300 and less than 0.700. In some embodiments M is Tb, and x is at least 0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Tb_(0.05)B₁₂. In some embodiments, the composite matrix is Zr_(0.90)Tb_(0.10)B₁₂. In some embodiments, the composite matrix is Zr_(0.85)Tb_(0.15)B₁₂. In some embodiments, the composite matrix is Zr_(0.80)Tb_(0.20)B₁₂. In some embodiments, the composite matrix is Zr_(0.75)Tb_(0.25)B₁₂. In some embodiments, the composite matrix is Zr_(0.70)Tb_(0.30)B₁₂. In some embodiments, the composite matrix is Zr_(0.65)Tb_(0.35)B₁₂. In some embodiments, the composite matrix is Zr_(0.60)Tb_(0.40)B₁₂. In some embodiments, the composite matrix is Zr_(0.55)Tb_(0.45)B₁₂. In some embodiments, the composite matrix is Zr_(0.50)Tb_(0.50)B₁₂. In some embodiments, the composite matrix is Zr_(0.45)Tb_(0.55)B₁₂. In some embodiments, the composite matrix is Zr_(0.40)Tb_(0.60)B₁₂. In some embodiments, the composite matrix is Zr_(0.35)Tb_(0.65)B₁₂. In some embodiments, the composite matrix is Zr_(0.30)Tb_(0.70)B₁₂. In some embodiments, the composite matrix is Zr_(0.25)Tb_(0.75)B₁₂. In some embodiments, the composite matrix is Zr_(0.20)Tb_(0.80)B₁₂. In some embodiments, the composite matrix is Zr_(0.15)Tb_(0.85)B₁₂. In some embodiments, the composite matrix is Zr_(0.10)Tb_(0.90)B₁₂. In some embodiments, the composite matrix is Zr_(0.05)Tb_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Tb_(0.05)B₁₂. In some embodiments, the composite matrix is Y_(0.90)Tb_(0.10)B₁₂. In some embodiments, the composite matrix is Y_(0.85)Tb_(0.15)B₁₂. In some embodiments, the composite matrix is Y_(0.80)Tb_(0.20)B₁₂. In some embodiments, the composite matrix is Y_(0.75)Tb_(0.25)B₁₂. In some embodiments, the composite matrix is Y_(0.70)Tb_(0.30)B₁₂. In some embodiments, the composite matrix is Y_(0.65)Tb_(0.35)B₁₂. In some embodiments, the composite matrix is Y_(0.60)Tb_(0.40)B₁₂. In some embodiments, the composite matrix is Y_(0.55)Tb_(0.45)B₁₂. In some embodiments, the composite matrix is Y_(0.50)Tb_(0.50)B₁₂. In some embodiments, the composite matrix is Y_(0.45)Tb_(0.55)B₁₂. In some embodiments, the composite matrix is Y_(0.40)Tb_(0.60)B₁₂. In some embodiments, the composite matrix is Y_(0.35)Tb_(0.65)B₁₂. In some embodiments, the composite matrix is Y_(0.30)Tb_(0.70)B₁₂. In some embodiments, the composite matrix is Y_(0.25)Tb_(0.75)B₁₂. In some embodiments, the composite matrix is Y_(0.20)Tb_(0.80)B₁₂. In some embodiments, the composite matrix is Y_(0.15)Tb_(0.85)B₁₂. In some embodiments, the composite matrix is Y_(0.10)Tb_(0.90)B₁₂. In some embodiments, the composite matrix is Y_(0.05)Tb_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Tb_(0.05)B₁₂. In some embodiments, the composite matrix is Sc_(0.90)Tb_(0.10)B₁₂. In some embodiments, the composite matrix is Sc_(0.85)Tb_(0.15)B₁₂. In some embodiments, the composite matrix is Sc_(0.80)Tb_(0.20)B₁₂. In some embodiments, the composite matrix is Sc_(0.75)Tb_(0.25)B₁₂. In some embodiments, the composite matrix is Sc_(0.70)Tb_(0.30)B₁₂. In some embodiments, the composite matrix is Sc_(0.65)Tb_(0.35)B₁₂. In some embodiments, the composite matrix is Sc_(0.60)Tb_(0.40)B₁₂. In some embodiments, the composite matrix is Sc_(0.55)Tb_(0.45)B₁₂. In some embodiments, the composite matrix is Sc_(0.50)Tb_(0.50)B₁₂. In some embodiments, the composite matrix is Sc_(0.45)Tb_(0.55)B₁₂. In some embodiments, the composite matrix is Sc_(0.40)Tb_(0.60)B₁₂. In some embodiments, the composite matrix is Sc_(0.35)Tb_(0.65)B₁₂. In some embodiments, the composite matrix is Sc_(0.30)Tb_(0.70)B₁₂. In some embodiments, the composite matrix is Sc_(0.25)Tb_(0.75)B₁₂. In some embodiments, the composite matrix is Sc_(0.20)Tb_(0.0312). In some embodiments, the composite matrix is Sc_(0.15)Tb_(0.85)B₁₂. In some embodiments, the composite matrix is Sc_(0.10)Tb_(0.90)B₁₂. In some embodiments, the composite matrix is Sc_(0.05)Tb_(0.95)B₁₂.

In some embodiments M is Dy, and x is at least 0.001 and less than 0.999. In some embodiments M is Dy, and x is at least 0.100 and less than 0.900. In some embodiments M is Dy, and x is at least 0.200 and less than 0.800. In some embodiments M is Dy, and x is at least 0.300 and less than 0.700. In some embodiments M is Dy, and x is at least 0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Dy_(0.05)B₁₂. In some embodiments, the composite matrix is Zr_(0.90)Dy_(0.10)B₁₂. In some embodiments, the composite matrix is Zr_(0.85)Dy_(0.15)B₁₂. In some embodiments, the composite matrix is Zr_(0.80)Dy_(0.20)B₁₂. In some embodiments, the composite matrix is Zr_(0.75)Dy_(0.25)B₁₂. In some embodiments, the composite matrix is Zr_(0.70)Dy_(0.30)B₁₂. In some embodiments, the composite matrix is Zr_(0.65)Dy_(0.35)B₁₂. In some embodiments, the composite matrix is Zr_(0.60)Dy_(0.40)B₁₂. In some embodiments, the composite matrix is Zr_(0.55)Dy_(0.45)B₁₂. In some embodiments, the composite matrix is Zr_(0.50)Dy_(0.50)B₁₂. In some embodiments, the composite matrix is Zr_(0.45)Dy_(0.55)B₁₂. In some embodiments, the composite matrix is Zr_(0.40)Dy_(0.60)B₁₂. In some embodiments, the composite matrix is Zr_(0.35)Dy_(0.65)B₁₂. In some embodiments, the composite matrix is Zr_(0.30)Dy_(0.70)B₁₂. In some embodiments, the composite matrix is Zr_(0.25)Dy_(0.75)B₁₂. In some embodiments, the composite matrix is Zr_(0.20)Dy_(0.80)B₁₂. In some embodiments, the composite matrix is Zr_(0.15)Dy_(0.0312). In some embodiments, the composite matrix is Zr_(0.10)Dy_(0.90)B₁₂. In some embodiments, the composite matrix is Zr_(0.05)Dy_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Dy_(0.05)B₁₂. In some embodiments, the composite matrix is Y_(0.90)Dy_(0.10)B₁₂. In some embodiments, the composite matrix is Y_(0.85)Dy 0.15B₁₂. In some embodiments, the composite matrix is Y_(0.80)Dy_(0.20)B₁₂. In some embodiments, the composite matrix is Y_(0.75)Dy_(0.25)B₁₂. In some embodiments, the composite matrix is Y_(0.70)Dy_(0.30)B₁₂. In some embodiments, the composite matrix is Y_(0.65)Dy_(0.35)B₁₂. In some embodiments, the composite matrix is Y_(0.60)Dy_(0.40)B₁₂. In some embodiments, the composite matrix is Y_(0.55)Dy_(0.45)B₁₂. In some embodiments, the composite matrix is Y_(0.50)Dy_(0.50)B₁₂. In some embodiments, the composite matrix is Y_(0.45)Dy_(0.55)B₁₂. In some embodiments, the composite matrix is Y_(0.40)Dy_(0.60)B₁₂. In some embodiments, the composite matrix is Y_(0.35)Dy_(0.65)B₁₂. In some embodiments, the composite matrix is Y_(0.30)Dy_(0.70)B₁₂. In some embodiments, the composite matrix is Y_(0.25)Dy_(0.75)B₁₂. In some embodiments, the composite matrix is Y_(0.20)Dy_(0.0312). In some embodiments, the composite matrix is Y_(0.15)Dy_(0.85)B₁₂. In some embodiments, the composite matrix is Y_(0.10)Dy_(0.90)B₁₂. In some embodiments, the composite matrix is Y_(0.05)Dy_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Dy_(0.05)B₁₂. In some embodiments, the composite matrix is Sc_(0.90)Dy_(0.10)B₁₂. In some embodiments, the composite matrix is Sc_(0.85)Dy 0.15B₁₂. In some embodiments, the composite matrix is Sc_(0.80)Dy_(0.20)B₁₂. In some embodiments, the composite matrix is Sc_(0.75)Dy_(0.25)B₁₂. In some embodiments, the composite matrix is Sc_(0.70)Dy_(0.30)B₁₂. In some embodiments, the composite matrix is Sc_(0.65)Dy_(0.35)B₁₂. In some embodiments, the composite matrix is Sc_(0.60)Dy_(0.40)B₁₂. In some embodiments, the composite matrix is Sc_(0.55)Dy_(0.45)B₁₂. In some embodiments, the composite matrix is Sc_(0.50)Dy_(0.50)B₁₂. In some embodiments, the composite matrix is Sc_(0.45)Dy_(0.55)B₁₂. In some embodiments, the composite matrix is Sc_(0.40)Dy_(0.60)B₁₂. In some embodiments, the composite matrix is Sc_(0.35)Dy_(0.65)B₁₂. In some embodiments, the composite matrix is Sc_(0.30)Dy_(0.70)B₁₂. In some embodiments, the composite matrix is Sc_(0.25)Dy_(0.75)B₁₂. In some embodiments, the composite matrix is Sc_(0.20)Dy_(0.0312). In some embodiments, the composite matrix is Sc_(0.15)Dy_(0.03)B₁₂. In some embodiments, the composite matrix is Sc_(0.10)Dy_(0.90)B₁₂. In some embodiments, the composite matrix is Sc_(0.05)Dy_(0.95)B₁₂.

In some embodiments M is Ho, and x is at least 0.001 and less than 0.999. In some embodiments M is Ho, and x is at least 0.100 and less than 0.900. In some embodiments M is Ho, and x is at least 0.200 and less than 0.800. In some embodiments M is Ho, and x is at least 0.300 and less than 0.700. In some embodiments M is Ho, and x is at least 0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Ho_(0.05)B₁₂. In some embodiments, the composite matrix is Zr_(0.90)Ho_(0.10)B₁₂. In some embodiments, the composite matrix is Zr_(0.85)Ho_(0.15)B₁₂. In some embodiments, the composite matrix is Zr_(0.80)Ho_(0.20)B₁₂. In some embodiments, the composite matrix is Zr_(0.75)Ho_(0.25)B₁₂. In some embodiments, the composite matrix is Zr_(0.70)Ho_(0.30)B₁₂. In some embodiments, the composite matrix is Zr_(0.65)Ho_(0.35)B₁₂. In some embodiments, the composite matrix is Zr_(0.60)H00.40B₁₂. In some embodiments, the composite matrix is Zr_(0.55)Ho_(0.45)B₁₂. In some embodiments, the composite matrix is Zr_(0.50)Ho_(0.50)B₁₂. In some embodiments, the composite matrix is Zr_(0.45)Ho_(0.55)B₁₂. In some embodiments, the composite matrix is Zr_(0.40)Ho_(0.60)B₁₂. In some embodiments, the composite matrix is Zr_(0.35)Ho_(0.65)B₁₂. In some embodiments, the composite matrix is Zr_(0.30)H00.70B₁₂. In some embodiments, the composite matrix is Zr_(0.25)Ho_(0.75)B₁₂. In some embodiments, the composite matrix is Zr_(0.20)Ho_(0.80)B₁₂. In some embodiments, the composite matrix is Zr_(0.15)Ho_(0.85)B₁₂. In some embodiments, the composite matrix is Zr_(0.10)Ho_(0.90)B₁₂. In some embodiments, the composite matrix is Zr_(0.05)Ho_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Ho_(0.05)B₁₂. In some embodiments, the composite matrix is Y_(0.90)Ho_(0.10)B₁₂. In some embodiments, the composite matrix is Y_(0.85)Ho_(0.15)B₁₂. In some embodiments, the composite matrix is Y_(0.80)Ho_(0.20)B₁₂. In some embodiments, the composite matrix is Y_(0.75)Ho_(0.25)B₁₂. In some embodiments, the composite matrix is Y_(0.70)Ho_(0.30)B₁₂. In some embodiments, the composite matrix is Y_(0.65)Ho_(0.35)B₁₂. In some embodiments, the composite matrix is Y_(0.60)Ho_(0.40)B₁₂. In some embodiments, the composite matrix is Y_(0.55)Ho_(0.45)B₁₂. In some embodiments, the composite matrix is Y_(0.50)Ho_(0.50)B₁₂. In some embodiments, the composite matrix is Y_(0.45)Ho_(0.55)B₁₂. In some embodiments, the composite matrix is Y_(0.40)Ho_(0.60)B₁₂. In some embodiments, the composite matrix is Y_(0.35)Ho_(0.65)B₁₂. In some embodiments, the composite matrix is Y_(0.30)Ho_(0.70)B₁₂. In some embodiments, the composite matrix is Y_(0.25)Ho_(0.75)B₁₂. In some embodiments, the composite matrix is Y_(0.20)Ho_(0.0312). In some embodiments, the composite matrix is Y_(0.15)Ho_(0.85)B₁₂. In some embodiments, the composite matrix is Y_(0.10)Ho_(0.90)B₁₂. In some embodiments, the composite matrix is Y_(0.05)Ho_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Ho_(0.05)B₁₂. In some embodiments, the composite matrix is Sc_(0.90)Ho_(0.10)B₁₂. In some embodiments, the composite matrix is Sc_(0.85)Ho_(0.15)B₁₂. In some embodiments, the composite matrix is Sc_(0.80)Ho_(0.20)B₁₂. In some embodiments, the composite matrix is Sc_(0.75)Ho_(0.25)B₁₂. In some embodiments, the composite matrix is Sc_(0.70)Ho_(0.30)B₁₂. In some embodiments, the composite matrix is Sc_(0.65)Ho_(0.35)B₁₂. In some embodiments, the composite matrix is Sc_(0.60)Ho_(0.40)B₁₂. In some embodiments, the composite matrix is Sc_(0.55)Ho_(0.45)B₁₂. In some embodiments, the composite matrix is Sc_(0.50)Ho_(0.50)B₁₂. In some embodiments, the composite matrix is Sc_(0.45)Ho_(0.55)B₁₂. In some embodiments, the composite matrix is Sc_(0.40)Ho_(0.60)B₁₂. In some embodiments, the composite matrix is Sc_(0.35)Ho_(0.65)B₁₂. In some embodiments, the composite matrix is Sc_(0.30)Ho_(0.70)B₁₂. In some embodiments, the composite matrix is Sc_(0.25)Ho_(0.75)B₁₂. In some embodiments, the composite matrix is Sc_(0.20)Ho_(0.80)B₁₂. In some embodiments, the composite matrix is Sc_(0.15)Ho_(0.0312). In some embodiments, the composite matrix is Sc_(0.10)Ho_(0.90)B₁₂. In some embodiments, the composite matrix is Sc_(0.05)Ho_(0.95)B₁₂.

In some embodiments M is Er, and x is at least 0.001 and less than 0.999. In some embodiments M is Er, and x is at least 0.100 and less than 0.900. In some embodiments M is Er, and x is at least 0.200 and less than 0.800. In some embodiments M is Er, and x is at least 0.300 and less than 0.700. In some embodiments M is Er, and x is at least 0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Er_(0.05)B₁₂. In some embodiments, the composite matrix is Zr_(0.90)Er_(0.10)B₁₂. In some embodiments, the composite matrix is Zr_(0.85)Er_(0.15)B₁₂. In some embodiments, the composite matrix is Zr_(0.80)Er_(0.20)B₁₂. In some embodiments, the composite matrix is Zr_(0.75)Er_(0.25)B₁₂. In some embodiments, the composite matrix is Zr_(0.70)Er_(0.30)B₁₂. In some embodiments, the composite matrix is Zr_(0.65)Er_(0.35)B₁₂. In some embodiments, the composite matrix is Zr_(0.60)Er_(0.40)B₁₂. In some embodiments, the composite matrix is Zr_(0.55)Er_(0.45)B₁₂. In some embodiments, the composite matrix is Zr_(0.50)Er_(0.50)B₁₂. In some embodiments, the composite matrix is Zr_(0.45)Er_(0.55)B₁₂. In some embodiments, the composite matrix is Zr_(0.40)Er_(0.60)B₁₂. In some embodiments, the composite matrix is Zr_(0.35)Er_(0.65)B₁₂. In some embodiments, the composite matrix is Zr_(0.30)Er_(0.70)B₁₂. In some embodiments, the composite matrix is Zr_(0.25)Er_(0.75)B₁₂. In some embodiments, the composite matrix is Zr_(0.20)Er_(0.80)B₁₂. In some embodiments, the composite matrix is Zr_(0.15)Er_(0.85)B₁₂. In some embodiments, the composite matrix is Zr_(0.10)Er_(0.90)B₁₂. In some embodiments, the composite matrix is Zr_(0.05)Er_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Er_(0.05)B₁₂. In some embodiments, the composite matrix is Y_(0.90)Er_(0.10)B₁₂. In some embodiments, the composite matrix is Y_(0.85)Er_(0.15)B₁₂. In some embodiments, the composite matrix is Y_(0.80)Er_(0.20)B₁₂. In some embodiments, the composite matrix is Y_(0.75)Er_(0.25)B₁₂. In some embodiments, the composite matrix is Y_(0.70)Er_(0.30)B₁₂. In some embodiments, the composite matrix is Y_(0.65)Er_(0.35)B₁₂. In some embodiments, the composite matrix is Y_(0.60)Er_(0.40)B₁₂. In some embodiments, the composite matrix is Y_(0.55)Er_(0.45)B₁₂. In some embodiments, the composite matrix is Y_(0.50)Er_(0.50)B₁₂. In some embodiments, the composite matrix is Y_(0.45)Er_(0.55)B₁₂. In some embodiments, the composite matrix is Y_(0.40)Er_(0.60)B₁₂. In some embodiments, the composite matrix is Y_(0.35)Er_(0.65)B₁₂. In some embodiments, the composite matrix is Y_(0.30)Er_(0.70)B₁₂. In some embodiments, the composite matrix is Y_(0.25)Er_(0.75)B₁₂. In some embodiments, the composite matrix is Y_(0.20)Er_(0.80)B₁₂. In some embodiments, the composite matrix is Y_(0.15)Er_(0.85)B₁₂. In some embodiments, the composite matrix is Y_(0.10)Er_(0.90)B₁₂. In some embodiments, the composite matrix is Y_(0.05)Er_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Er_(0.05)B₁₂. In some embodiments, the composite matrix is Sc_(0.90)Er_(0.10)B₁₂. In some embodiments, the composite matrix is Sc_(0.85)Er_(0.15)B₁₂. In some embodiments, the composite matrix is Sc_(0.80)Er_(0.20)B₁₂. In some embodiments, the composite matrix is Sc_(0.75)Er_(0.25)B₁₂. In some embodiments, the composite matrix is Sc_(0.70)Er_(0.30)B₁₂. In some embodiments, the composite matrix is Sc_(0.65)Er_(0.35)B₁₂. In some embodiments, the composite matrix is Sc_(0.60)Er_(0.40)B₁₂. In some embodiments, the composite matrix is Sc_(0.55)Er_(0.45)B₁₂. In some embodiments, the composite matrix is Sc_(0.50)Er_(0.50)B₁₂. In some embodiments, the composite matrix is Sc_(0.45)Er_(0.55)B₁₂. In some embodiments, the composite matrix is Sc_(0.40)Er_(0.60)B₁₂. In some embodiments, the composite matrix is Sc_(0.35)Er_(0.65)B₁₂. In some embodiments, the composite matrix is Sc_(0.30)Er_(0.70)B₁₂. In some embodiments, the composite matrix is Sc_(0.25)Er_(0.75)B₁₂. In some embodiments, the composite matrix is Sc_(0.20)Er_(0.0312). In some embodiments, the composite matrix is Sc_(0.15)Er_(0.85)B₁₂. In some embodiments, the composite matrix is Sc_(0.10)Er_(0.90)B₁₂. In some embodiments, the composite matrix is Sc_(0.05)Er_(0.95)B₁₂.

In some embodiments M is Tm, and x is at least 0.001 and less than 0.999. In some embodiments M is Tm, and x is at least 0.100 and less than 0.900. In some embodiments M is Tm, and x is at least 0.200 and less than 0.800. In some embodiments M is Tm, and x is at least 0.300 and less than 0.700. In some embodiments M is Tm, and x is at least 0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Tm_(0.05)B₁₂. In some embodiments, the composite matrix is Zr_(0.90)Tm_(0.10)B₁₂. In some embodiments, the composite matrix is Zr_(0.85)Tm_(0.15)B₁₂. In some embodiments, the composite matrix is Zr_(0.80)Tm_(0.20)B₁₂. In some embodiments, the composite matrix is Zr_(0.75) Tm_(0.25)B₁₂. In some embodiments, the composite matrix is Zr_(0.70)Tm_(0.30)B₁₂. In some embodiments, the composite matrix is Zr_(0.65)Tm_(0.35)B₁₂. In some embodiments, the composite matrix is Zr_(0.60)Tm_(0.40)B₁₂. In some embodiments, the composite matrix is Zr_(0.55)Tm_(0.45)B₁₂. In some embodiments, the composite matrix is Zr_(0.50)Tm_(0.50)B₁₂. In some embodiments, the composite matrix is Zr_(0.45) Tm_(0.55)B₁₂. In some embodiments, the composite matrix is Zr_(0.40)Tm_(0.60)B₁₂. In some embodiments, the composite matrix is Zr_(0.35)Tm_(0.65)B₁₂. In some embodiments, the composite matrix is Zr_(0.30)Tm 0.70B₁₂. In some embodiments, the composite matrix is Zr_(0.25)Tm_(0.75)B₁₂. In some embodiments, the composite matrix is Zr_(0.20)Tm_(0.80)B₁₂. In some embodiments, the composite matrix is Zr_(0.15)Tm_(0.0312). In some embodiments, the composite matrix is Zr_(0.10)Tm_(0.90)B₁₂. In some embodiments, the composite matrix is Zr_(0.05)Tm_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Tm_(0.05)B₁₂. In some embodiments, the composite matrix is Y_(0.90)Tm_(0.10)B₁₂. In some embodiments, the composite matrix is Y_(0.85)Tm_(0.15)B₁₂. In some embodiments, the composite matrix is Y_(0.80)Tm_(0.20)B₁₂. In some embodiments, the composite matrix is Y_(0.75) Tm_(0.25)B₁₂. In some embodiments, the composite matrix is Y_(0.70)Tm_(0.30)B₁₂. In some embodiments, the composite matrix is Y_(0.65)Tm_(0.35)B₁₂. In some embodiments, the composite matrix is Y_(0.60) Tm_(0.40)B₁₂. In some embodiments, the composite matrix is Y_(0.55)Tm_(0.45)B₁₂. In some embodiments, the composite matrix is Y_(0.50)Tm_(0.50)B₁₂. In some embodiments, the composite matrix is Y_(0.45) Tm_(0.55)B₁₂. In some embodiments, the composite matrix is Y_(0.40) Tm_(0.60)B₁₂. In some embodiments, the composite matrix is Y_(0.35)Tm_(0.65)B₁₂. In some embodiments, the composite matrix is Y_(0.30) Tm_(0.70)B₁₂. In some embodiments, the composite matrix is Y_(0.25)Tm_(0.75)B₁₂. In some embodiments, the composite matrix is Y_(0.20)Tm_(0.80)B₁₂. In some embodiments, the composite matrix is Y_(0.15)Tm_(0.85)B₁₂. In some embodiments, the composite matrix is Y_(0.10)Tm_(0.90)B₁₂. In some embodiments, the composite matrix is Y_(0.05)Tm_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Tm_(0.05)B₁₂. In some embodiments, the composite matrix is Sc_(0.90)Tm_(0.10)B₁₂. In some embodiments, the composite matrix is Sc_(0.85)Tm_(0.15)B₁₂. In some embodiments, the composite matrix is Sc_(0.80)Tm_(0.20)B₁₂. In some embodiments, the composite matrix is Sc_(0.75)Tm_(0.25)B₁₂. In some embodiments, the composite matrix is Sc_(0.70)Tm_(0.30)B₁₂. In some embodiments, the composite matrix is Sc_(0.65)Tm_(0.35)B₁₂. In some embodiments, the composite matrix is Sc_(0.60)Tm_(0.40)B₁₂. In some embodiments, the composite matrix is Sc_(0.55)Tm_(0.45)B₁₂. In some embodiments, the composite matrix is Sc_(0.50)Tm_(0.50)B₁₂. In some embodiments, the composite matrix is Sc_(0.45)Tm_(0.55)B₁₂. In some embodiments, the composite matrix is Sc_(0.40)Tm_(0.60)B₁₂. In some embodiments, the composite matrix is Sc_(0.35)Tm_(0.65)B₁₂. In some embodiments, the composite matrix is Sc_(0.30)Tm_(0.70)B₁₂. In some embodiments, the composite matrix is Sc_(0.25)Tm_(0.75)B₁₂. In some embodiments, the composite matrix is Sc_(0.20)Tm_(0.0312). In some embodiments, the composite matrix is Sc_(0.15)Tm_(0.85)B₁₂. In some embodiments, the composite matrix is Sc_(0.10)Tm_(0.90)B₁₂. In some embodiments, the composite matrix is Sc_(0.05)Tm_(0.95)B₁₂.

In some embodiments M is Yb, and x is at least 0.001 and less than 0.999. In some embodiments M is Yb, and x is at least 0.100 and less than 0.900. In some embodiments M is Yb, and x is at least 0.200 and less than 0.800. In some embodiments M is Yb, and x is at least 0.300 and less than 0.700. In some embodiments M is Yb, and x is at least 0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Yb_(0.05)B₁₂. In some embodiments, the composite matrix is Zr_(0.90)Yb_(0.10)B₁₂. In some embodiments, the composite matrix is Zr_(0.85)Yb_(0.15)B₁₂. In some embodiments, the composite matrix is Zr_(0.80)Yb_(0.20)B₁₂. In some embodiments, the composite matrix is Zr_(0.75)Yb_(0.25)B₁₂. In some embodiments, the composite matrix is Zr_(0.70)Yb_(0.30)B₁₂. In some embodiments, the composite matrix is Zr_(0.65)Yb_(0.35)B₁₂. In some embodiments, the composite matrix is Zr_(0.60)Yb_(0.40)B₁₂. In some embodiments, the composite matrix is Zr_(0.55)Yb_(0.45)B₁₂. In some embodiments, the composite matrix is Zr_(0.50)Yb_(0.50)B₁₂. In some embodiments, the composite matrix is Zr_(0.45)Yb_(0.55)B₁₂. In some embodiments, the composite matrix is Zr_(0.40)Yb_(0.60)B₁₂. In some embodiments, the composite matrix is Zr_(0.35)Yb_(0.65)B₁₂. In some embodiments, the composite matrix is Zr_(0.30)Yb_(0.70)B₁₂. In some embodiments, the composite matrix is Zr_(0.25)Yb_(0.75)B₁₂. In some embodiments, the composite matrix is Zr_(0.20)Yb_(0.80)B₁₂. In some embodiments, the composite matrix is Zr_(0.15)Yb_(0.0312). In some embodiments, the composite matrix is Zr_(0.10)Yb_(0.90)B₁₂. In some embodiments, the composite matrix is Zr_(0.05)Yb_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Yb_(0.05)B₁₂. In some embodiments, the composite matrix is Y_(0.90)Yb_(0.10)B₁₂. In some embodiments, the composite matrix is Y_(0.85)Yb_(0.15)B₁₂. In some embodiments, the composite matrix is Y_(0.80)Yb_(0.20)B₁₂. In some embodiments, the composite matrix is Y_(0.75)Yb_(0.25)B₁₂. In some embodiments, the composite matrix is Y_(0.70)Yb_(0.30)B₁₂. In some embodiments, the composite matrix is Y_(0.65)Yb_(0.35)B₁₂. In some embodiments, the composite matrix is Y_(0.60)Yb_(0.40)B₁₂. In some embodiments, the composite matrix is Y_(0.55)Yb_(0.45)B₁₂. In some embodiments, the composite matrix is Y_(0.50)Yb_(0.50)B₁₂. In some embodiments, the composite matrix is Y_(0.45)Yb_(0.55)B₁₂. In some embodiments, the composite matrix is Y_(0.40)Yb_(0.60)B₁₂. In some embodiments, the composite matrix is Y_(0.35)Yb_(0.65)B₁₂. In some embodiments, the composite matrix is Y_(0.30)Yb_(0.70)B₁₂. In some embodiments, the composite matrix is Y_(0.25)Yb_(0.75)B₁₂. In some embodiments, the composite matrix is Y_(0.20)Yb_(0.0312). In some embodiments, the composite matrix is Y_(0.15)Yb_(0.85)B₁₂. In some embodiments, the composite matrix is Y_(0.10)Yb_(0.90)B₁₂. In some embodiments, the composite matrix is Y_(0.05)Yb_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Yb_(0.05)B₁₂. In some embodiments, the composite matrix is Sc_(0.90)Yb_(0.10)B₂. In some embodiments, the composite matrix is Sc_(0.85)Yb_(0.15)B₁₂. In some embodiments, the composite matrix is Sc_(0.80)Yb_(0.20)B₁₂. In some embodiments, the composite matrix is Sc_(0.75)Yb_(0.25)B₁₂. In some embodiments, the composite matrix is Sc_(0.70)Yb_(0.30)B₁₂. In some embodiments, the composite matrix is Sc_(0.65)Yb_(0.35)B₁₂. In some embodiments, the composite matrix is Sc_(0.60)Yb_(0.40)B₁₂. In some embodiments, the composite matrix is Sc_(0.55)Yb_(0.45)B₁₂. In some embodiments, the composite matrix is Sc_(0.50)Yb_(0.50)B₁₂. In some embodiments, the composite matrix is Sc_(0.45)Yb_(0.55)B₁₂. In some embodiments, the composite matrix is Sc_(0.40)Yb_(0.60)B₁₂. In some embodiments, the composite matrix is Sc_(0.35)Yb_(0.65)B₁₂. In some embodiments, the composite matrix is Sc_(0.30)Yb_(0.70)B₁₂. In some embodiments, the composite matrix is Sc_(0.25)Yb_(0.75)B₁₂. In some embodiments, the composite matrix is Sc_(0.20)Yb_(0.80)B₁₂. In some embodiments, the composite matrix is Sc_(0.15)Yb_(0.0312). In some embodiments, the composite matrix is Sc_(0.10)Yb_(0.90)B₁₂. In some embodiments, the composite matrix is Sc_(0.05)Yb_(0.95)B₁₂.

In some embodiments M is Lu, and x is at least 0.001 and less than 0.999. In some embodiments M is Lu, and x is at least 0.100 and less than 0.900. In some embodiments M is Lu, and x is at least 0.200 and less than 0.800. In some embodiments M is Lu, and x is at least 0.300 and less than 0.700. In some embodiments M is Lu, and x is at least 0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Lu_(0.05)B₁₂. In some embodiments, the composite matrix is Zr_(0.90)Lu_(0.10)B₁₂. In some embodiments, the composite matrix is Zr_(0.85)Lu_(0.15)B₁₂. In some embodiments, the composite matrix is Zr_(0.80)Lu_(0.20)B₁₂. In some embodiments, the composite matrix is Zr_(0.75)Lu_(0.25)B₁₂. In some embodiments, the composite matrix is Zr_(0.70)Lu_(0.30)B₁₂. In some embodiments, the composite matrix is Zr_(0.65)Lu_(0.35)B₁₂. In some embodiments, the composite matrix is Zr_(0.60)Lu_(0.40)B₁₂. In some embodiments, the composite matrix is Zr_(0.55)Lu_(0.45)B₁₂. In some embodiments, the composite matrix is Zr_(0.50)Lu_(0.50)B₁₂. In some embodiments, the composite matrix is Zr_(0.45)Lu_(0.55)B₁₂. In some embodiments, the composite matrix is ZroAo Lu_(0.60)B₁₂. In some embodiments, the composite matrix is Zr_(0.35)Lu_(0.65)B₁₂. In some embodiments, the composite matrix is Zr_(0.30)Lu_(0.70)B₁₂. In some embodiments, the composite matrix is Zr_(0.25)Lu_(0.75)B₁₂. In some embodiments, the composite matrix is Zr_(0.20)Lu_(0.80)B₁₂. In some embodiments, the composite matrix is Zr_(0.15)Lu_(0.85)B₁₂. In some embodiments, the composite matrix is Zr_(0.10)Lu_(0.90)B₁₂. In some embodiments, the composite matrix is Zr_(0.05)Lu_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Lu_(0.05)B₁₂. In some embodiments, the composite matrix is Y_(0.90)Lu_(0.10)B₁₂. In some embodiments, the composite matrix is Y_(0.85)Lu_(0.15)B₁₂. In some embodiments, the composite matrix is Y_(0.80)Lu_(0.20)B₁₂. In some embodiments, the composite matrix is Y_(0.75)Lu_(0.25)B₁₂. In some embodiments, the composite matrix is Y_(0.70)Lu_(0.30)B₁₂. In some embodiments, the composite matrix is Y_(0.65)Lu_(0.35)B₁₂. In some embodiments, the composite matrix is Y_(0.60)Lu_(0.40)B₁₂. In some embodiments, the composite matrix is Y_(0.55)Lu_(0.45)B₁₂. In some embodiments, the composite matrix is Y_(0.50)Lu_(0.50)B₁₂. In some embodiments, the composite matrix is Y_(0.45)Lu_(0.55)B₁₂. In some embodiments, the composite matrix is Y_(0.40)Lu_(0.60)B₁₂. In some embodiments, the composite matrix is Y_(0.35)Lu_(0.65)B₁₂. In some embodiments, the composite matrix is Y_(0.30)Lu_(0.70)B₁₂. In some embodiments, the composite matrix is Y_(0.25)Lu_(0.75)B₁₂. In some embodiments, the composite matrix is Y_(0.20)Lu_(0.80)B₁₂. In some embodiments, the composite matrix is Y_(0.15)Lu_(0.85)B₁₂. In some embodiments, the composite matrix is Y_(0.10)Lu_(0.90)B₁₂. In some embodiments, the composite matrix is Yoms Lu_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Lu_(0.05)B₁₂. In some embodiments, the composite matrix is Sc_(0.90)Lu_(0.10)B₁₂. In some embodiments, the composite matrix is Sc_(0.85)Lu_(0.15)B₁₂. In some embodiments, the composite matrix is Sc_(0.80)Lu_(0.20)B₁₂. In some embodiments, the composite matrix is Sc_(0.75)Lu_(0.25)B₁₂. In some embodiments, the composite matrix is Sc_(0.70)Lu_(0.30)B₁₂. In some embodiments, the composite matrix is Sc_(0.65)Lu_(0.35)B₁₂. In some embodiments, the composite matrix is Sc_(0.60)Lu_(0.40)B₁₂. In some embodiments, the composite matrix is Sc_(0.55)Lu_(0.45)B₁₂. In some embodiments, the composite matrix is Sc_(0.50)Lu_(0.50)B₁₂. In some embodiments, the composite matrix is Sc_(0.45)Lu_(0.55)B₁₂. In some embodiments, the composite matrix is Sc_(0.40)Lu_(0.60)B₁₂. In some embodiments, the composite matrix is Sc_(0.35)Lu_(0.65)B₁₂. In some embodiments, the composite matrix is Sc_(0.30)Lu_(0.70)B₁₂. In some embodiments, the composite matrix is Sc_(0.25)Lu_(0.75)B₁₂. In some embodiments, the composite matrix is Sc_(0.20)Lu_(0.80)B₁₂. In some embodiments, the composite matrix is Sc_(0.15)Lu_(0.85)B₁₂. In some embodiments, the composite matrix is Sc_(0.10)Lu_(0.90)B₁₂. In some embodiments, the composite matrix is Sc_(0.05)Lu_(0.95)B₁₂.

In some embodiments, the hardness described herein is measured by a Vickers hardness test. In some embodiments, the hardness is measured under a load of 0.49 Newton (N).

In some embodiments, a composite matrix described herein has a hardness of about 10 to about 70 GPa. In some embodiments, a composite matrix described herein has a hardness of about 10 to about 60 GPa, about 10 to about 50 GPa, about 10 to about 40 GPa, about 10 to about 30GPa, about 20 to about 70 GPa, about 20 to about 60 GPa, about 20 to about 50 GPa, about 20 to about 40 GPa, about 20 to about 30 GPa, about 30 to about 70 GPa, about 30 to about 60 GPa, about 30 to about 50 GPa, about 30 to about 45 GPa, about 30 to about 40 GPa, about 30 to about 35 GPa, about 35 to about 70 GPa, about 35 to about 60 GPa, about 35 to about 50 GPa, about 35 to about 40 GPa, about 40 to about 70 GPa, about 40 to about 60 GPa, about 40 to about 50 GPa, about 45 to about 60 GPa or about 45 to about 50 GPa. In some embodiments, a composite matrix described herein has a hardness of about 30 to about 50 GPa, about 30 to about 45 GPa, about 30 to about 40 GPa, about 30 to about 35 GPa, about 35 to about 50 GPa, about 35 to about 40 GPa, about 40 to about 50 GPa, or about 45 to about 50 GPa.

In some embodiments, a composite matrix described herein has a hardness of about 10 GPa, about 15 GPa, about 20 GPa, about 25 GPa, about 30 GPa, about 31 GPa, about 32 GPa, about 33 GPa, about 34 GPa, about 35 GPa, about 36 GPa, about 37 GPa, about 38 GPa, about 39 GPa, about 40 GPa, about 41 GPa, about 42 GPa, about 43 GPa, about 44 GPa, about 45 GPa, about 46 GPa, about 47 GPa, about 48 GPa, about 49 GPa, about 50 GPa, about 51 GPa, about 52 GPa, about 53 GPa, about 54 GPa, about 55 GPa, about 56 GPa, about 57 GPa, about 58 GPa, about 59 GPa, about 60 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 10 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 15 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 20 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 25 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 30 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 31 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 32 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 33 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 34 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 35 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 36 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 37 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 38 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 39 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 40 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 41 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 42 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 43 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 44 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 45 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 46 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 47 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 48 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 49 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 50 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 51 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 52 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 53 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 54 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 55 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 56 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 57 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 58 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 59 GPa or higher. In some embodiments, a composite matrix described herein has a hardness of about 60 GPa or higher.

In some embodiments, a composite matrix described herein has a hardness between 38.0 and 52.0 GPa.

In some embodiments, a composite matrix is Zr_(1-x)Y_(x)B₁₂ and has a hardness between 38.0 and 52.0 GPa. In some embodiments, a composite matrix is Zr_(1-x)Y_(x)B₁₂ and has a hardness between 40.0 and 50.0 GPa. In some embodiments, a composite matrix is Zr_(1-x)Y_(x)B₁₂ and has a hardness between 42.0 and 48.0 GPa. In some embodiments, a composite matrix is Zr_(1-x)Y_(x)B₁₂ and has a hardness between 44.0 and 48.0 GPa. In some embodiments, a composite matrix is Zr_(1-x)Y_(x)B₁₂ and has a hardness between 45.0 and 46.0 GPa.

In some embodiments, a composite matrix is Zr_(1-x)Sc_(x)B₁₂ and has a hardness between 38.0 and 52.0 GPa. In some embodiments, a composite matrix is Zr_(1-x)Sc_(x)B₁₂ and has a hardness between 45.0 and 51.0 GPa. In some embodiments, a composite matrix is Zr_(1-x)Sc_(x)B₁₂ and has a hardness between 46.0 and 50.0 GPa. In some embodiments, a composite matrix is Zr_(1-x)Sc_(x)B₁₂ and has a hardness between 47.0 and 49.0 GPa.

In some embodiments, a composite matrix is Y_(1-x)Sc_(x)B₁₂ and has a hardness between 38.0 and 52.0 GPa. In some embodiments, a composite matrix is Y_(1-x)Sc_(x)B₁₂ and has a hardness between 40.0 and 50.0 GPa. In some embodiments, a composite matrix is Y_(1-x)Sc_(x)B₁₂ and has a hardness between 42.0 and 48.0 GPa. In some embodiments, a composite matrix is Y_(1-x)Sc_(x)B₁₂ and has a hardness between 44.0 and 46.0 GPa.

In some embodiments, a composite matrix is Zr_(1-x)Gd_(x)B₁₂ and has a hardness between 38.0 and 52.0 GPa. In some embodiments, a composite matrix is Zr_(1-x)Gd_(x)B₁₂ and has a hardness between 38.0 and 45.0 GPa. In some embodiments, a composite matrix is Zr_(1-x)Gd_(x)B₁₂ and has a hardness between 39.0 and 44.0 GPa. In some embodiments, a composite matrix is Zr_(1-x)Gd_(x)B₁₂ and has a hardness between 40.0 and 44.0 GPa. In some embodiments, a composite matrix is Zr_(1-x)Gd_(x)B₁₂ and has a hardness between 41.0 and 43.0 GPa.

In some embodiments, a composite matrix described herein has a grain size of about 20 μm or less. In some embodiments, the composite matrix has a grain size of about 15 μm or less, about 12 μm or less, about 10 μm or less, about 8 μm or less, about 5 μm or less, about 2 μm or less or about 1 μm or less. In some embodiments, the composite matrix has a grain size of about 15 μm or less. In some embodiments, the composite matrix has a grain size of about 12 μm or less. In some embodiments, the composite matrix has a grain size of about 10 μm or less. In some embodiments, the composite matrix has a grain size of about 9 μm or less. In some embodiments, the composite matrix has a grain size of about 8 μm or less. In some embodiments, the composite matrix has a grain size of about 7 μm or less. In some embodiments, the composite matrix has a grain size of about 6 μm or less. In some embodiments, the composite matrix has a grain size of about 5 μm or less. In some embodiments, the composite matrix has a grain size of about 4 μm or less. In some embodiments, the composite matrix has a grain size of about 3 μm or less. In some embodiments, the composite matrix has a grain size of about 2 μm or less. In some embodiments, the composite matrix has a grain size of about 1 μum or less.

In some embodiments, the grain size is an averaged grain size. In some embodiments, a composite matrix described herein has an averaged grain size of about 20 μm or less. In some embodiments, the composite matrix has an averaged grain size of about 15 μm or less, about 12 μm or less, about 10 μm or less, about 8 μm or less, about 5 μm or less, about 2 μm or less or about 1 μm or less. In some embodiments, the composite matrix has an averaged grain size of about 15 μm or less. In some embodiments, the composite matrix has an averaged grain size of about 12 μm or less. In some embodiments, the composite matrix has an averaged grain size of about 10 μm or less. In some embodiments, the composite matrix has an averaged grain size of about 9 μm or less. In some embodiments, the composite matrix has an averaged grain size of about 8 μm or less. In some embodiments, the composite matrix has an averaged grain size of about 7 μm or less. In some embodiments, the composite matrix has an averaged grain size of about 6 μm or less. In some embodiments, the composite matrix has an averaged grain size of about 5 μm or less. In some embodiments, the composite matrix has an averaged grain size of about 4 μm or less. In some embodiments, the composite matrix has an averaged grain size of about 3 μm or less. In some embodiments, the composite matrix has an averaged grain size of about 2 μm or less. In some embodiments, the composite matrix has an averaged grain size of about 1 μm or less.

In some embodiments, a composite matrix described herein is a densified composite matrix. In some embodiments, a composite matrix described herein has a density of 10.0 g/cm³ or less. In some embodiments, a composite matrix described herein has a density of 9.0 g/cm³ or less. In some embodiments, a composite matrix described herein has a density of 8.0 g/cm³ or less. In some embodiments, a composite matrix described herein has a density of 7.0 g/cm³ or less. In some embodiments, a composite matrix described herein has a density of 6.0 g/cm³ or less. In some embodiments, a composite matrix described herein has a density of 5.0 g/cm³ or less. In some embodiments, a composite matrix described herein has a density of 4.0 g/cm³ or less. In some embodiments, a composite matrix described herein has a density of 3.55 g/cm³ or less. In some embodiments, a composite matrix described herein has a density of 3.0 g/cm³ or less.

In some embodiments, a composite matrix described herein has a density of or between 0.1-10.0 g/cm³. In some embodiments, a composite matrix described herein has a density of or between 1.0-9.0 g/cm³. In some embodiments, a composite matrix described herein has a density of or between 1.0-8.0 g/cm³. In some embodiments, a composite matrix described herein has a density of or between 1.0-7.0 g/cm³. In some embodiments, a composite matrix described herein has a density of or between 2.0-6.0 g/cm³. In some embodiments, a composite matrix described herein has a density of or between 2.0-5.0 g/cm³. In some embodiments, a composite matrix described herein has a density of or between 2.5-4.5 g/cm³. In some embodiments, a composite matrix described herein has a density of or between 3.0-4.0 g/cm³.

In some embodiments, a composite matrix of Zr_(1-x)Y_(x)B₁₂ has a density of 6.0 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Y_(x)B₁₂ has a density of 5.0 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Y_(x)B₁₂ has a density of 4.5 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Y_(x)B₁₂ has a density of 4.0 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Y_(x)B₁₂ has a density of 3.75 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Y_(x)B₁₂ has a density of 3.55 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Y_(x)B₁₂ has a density of 3.4 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Y_(x)B₁₂ has a density of 3.0 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Y_(x)B₁₂ has a density of 2.5 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Y_(x)B₁₂ has a density of 2.0 g/cm³ or less.

In some embodiments, a composite matrix of Zr_(1-x)Sc_(x)B₁₂ has a density of 6.0 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Sc_(x)B₁₂ has a density of 5.0 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Sc_(x)B₁₂ has a density of 4.0 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Sc_(x)B₁₂ has a density of 3.5 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Sc_(x)B₁₂ has a density of 3.35 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Sc_(x)B₁₂ has a density of 3.1 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Sc_(x)B₁₂ has a density of 3.0 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Sc_(x)B₁₂ has a density of 2.5 g/cm³ or less. In some embodiments, a composite matrix of Zr_(1-x)Sc_(x)B₁₂ has a density of 2.0 g/cm³ or less.

In some embodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of 6.0 g/cm³ or less. In some embodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of 5.0 g/cm³ or less. In some embodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of 4.0 g/cm³ or less. In some embodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of 3.5 g/cm³ or less. In some embodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of 3.3 g/cm³ or less. In some embodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of 3.21 g/cm³ or less. In some embodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of 3.1 g/cm³ or less. In some embodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of 3.0 g/cm³ or less. In some embodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of 2.75 g/cm³ or less. In some embodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of 2.50 g/cm³ or less. In some embodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of 2.0 g/cm³ or less.

In some embodiments, a composite material described herein is resistant to oxidation. In some embodiments, the composite matrix is resistant to oxidation below 550° C. In some embodiments, the composite matrix is resistant to oxidation below 570° C. In some embodiments, the composite matrix is resistant to oxidation below 590° C. In some embodiments, the composite matrix is resistant to oxidation below 600° C. In some embodiments, the composite matrix is resistant to oxidation below 610° C. In some embodiments, the composite matrix is resistant to oxidation below 620° C. In some embodiments, the composite matrix is resistant to oxidation below 630° C. In some embodiments, the composite matrix is resistant to oxidation below 640° C. In some embodiments, the composite matrix is resistant to oxidation below 650° C. In some embodiments, the composite matrix is resistant to oxidation below 660° C. In some embodiments, the composite matrix is resistant to oxidation below 665° C. In some embodiments, the composite matrix is resistant to oxidation below 670° C. In some embodiments, the composite matrix is resistant to oxidation below 675° C. In some embodiments, the composite matrix is resistant to oxidation below 680° C. In some embodiments, the composite matrix is resistant to oxidation below 685° C. In some embodiments, the composite matrix is resistant to oxidation below 690° C. In some embodiments, the composite matrix is resistant to oxidation below 695° C. In some embodiments, the composite matrix is resistant to oxidation below 700° C. In some embodiments, the composite matrix is resistant to oxidation below 725° C. In some embodiments, the composite matrix is resistant to oxidation below 750° C. In some embodiments, the composite matrix is resistant to oxidation below 775° C. In some embodiments, the composite matrix is resistant to oxidation below 800° C. In some embodiments, the composite matrix is resistant to oxidation below 825° C. In some embodiments, the composite matrix is resistant to oxidation below 850° C. In some embodiments, the composite matrix is resistant to oxidation below 875° C. In some embodiments, the composite matrix is resistant to oxidation below 900° C.

In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂ and resistant to oxidation below 600° C. In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂ and resistant to oxidation below 610° C. In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂ and resistant to oxidation below 620° C. In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂ and resistant to oxidation below 630° C. In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂ and resistant to oxidation below 640° C. In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂ and resistant to oxidation below 650° C.

In some embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 600° C. In some embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 620° C. In some embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 640° C. In some embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 660° C. In some embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 670° C. In some embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 675° C. In some embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 680° C. In some embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 700° C.

In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 600° C. In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 620° C. In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 640° C. In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 660° C. In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 670° C. In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 675° C. In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 680° C. In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 685° C. In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 690° C. In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 695° C. In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 700° C. In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 710° C. In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 720° C.

In some embodiments, a composite material described herein is resistant to oxidation. In some embodiments, a composite material described herein has anti-oxidation property. For example, when the composite material is coated on the surface of a tool, the composite material reduces the rate of oxidation of the tool in comparison to a tool not coated with the composite material. In an alternative example, when the composite material is coated on the surface of a tool, the composite material prevents oxidation of the tool in comparison to a tool not coated with the composite material. In some embodiments, the composite material inhibits the formation of oxidation or reduces the rate of oxidation.

In some embodiments, a composite matrix described herein is cubic or tetragonal as determined and characterized by X-ray diffraction. In some embodiments, a composite matrix described herein is cubic. In some embodiments, a composite matrix described herein is cubic and the length of a is between 7.350 and 7.550 Å, where a is the length between two adjacent vertices in the unit cell.

In some embodiments, a composite matrix described herein is tetragonal. In some embodiments, a composite matrix is tetragonal and the length of a is between 5.150 and 5.450 Å, where a is the shortest length between two adjacent vertices in the unit cell, and the length of c is between 7.350 and 7.550 Å, where c is the longest length between two adjacent vertices in the unit cell.

In some embodiments, a composite matrix Zr_(1-x)Y_(x)B₁₂ is cubic and the length of a is between 7.350 and 7.550 Å, where a is the length between two adjacent vertices in the unit cell. In some embodiments, a composite matrix Zr_(1-x)Gd_(x)B₁₂ is cubic and the length of a is between 7.350 and 7.550 Å, where a is the length between two adjacent vertices in the unit cell. In some embodiments, a composite matrix Zr_(1-x)Sm_(x)B₁₂ is cubic and the length of a is between 7.350 and 7.550 Å, where a is the length between two adjacent vertices in the unit cell. In some embodiments, a composite matrix Zr_(1-x)Nd_(x)B₁₂ is cubic and the length of a is between 7.350 and 7.550 Å, where a is the length between two adjacent vertices in the unit cell. In some embodiments, a composite matrix Zr_(1-x)Pr_(x)B₁₂ is cubic and the length of a is between 7.350 and 7.550 Å, where a is the length between two adjacent vertices in the unit cell. In some embodiments, a composite matrix Zr_(1-x)Sc_(x)B₁₂ is tetragonal and the length of a is between 5.150 and 5.450 Å, where a is the shortest length between two adjacent vertices in the unit cell, and the length of c is between 7.350 and 7.550 Å, where c is the longest length between two adjacent vertices in the unit cell. In some embodiments, a composite matrix Y_(1-x)Sc_(x)B₁₂ is tetragonal and the length of a is between 5.150 and 5.450 Å, where a is the shortest length between two adjacent vertices in the unit cell, and the length of c is between 7.350 and 7.550 Å, where c is the longest length between two adjacent vertices in the unit cell.

In some embodiments, a composite matrix described herein comprises a solid solution phase. In some embodiments, a composite material described herein forms a solid solution.

Methods of Manufacture

Certain embodiments described herein include methods of making a composite matrix. Some embodiments described herein comprise a method of preparing an oxidative resistant composite matrix, which comprises (a) blending together the boron and metals for a time sufficient to produce a powder mixture; (b) pressing the powder mixture under a pressure sufficient to generate a pellet; and (c) sintering the pellet at a temperature sufficient to produce a densified composite matrix.

In some embodiments, the blending time is about 5 minutes to about 6 hours. In some embodiments, the blending time is about 5 minutes, about 10 minutes, about 15 minutes, about 20 minutes, about 30 minutes, about 45 minutes, about 1 hour, about 1.5 hour, about 2 hours, about 3 hours, about 4 hours, about 5 hours, or about 6 hours.

In some embodiments, the blending time is at least 5 minutes or more. In some embodiments, the blending time is about 10 minutes or more. In some embodiments, the blending time is about 20 minutes or more. In some embodiments, the blending time is about 30 minutes or more. In some embodiments, the blending time is about 45 minutes or more. In some embodiments, the blending time is about 1 hour or more. In some embodiments, the blending time is about 2 hours or more. In some embodiments, the blending time is about 3 hours or more. In some embodiments, the blending time is about 4 hours or more. In some embodiments, the blending time is about 5 hours or more. In some embodiments, the blending time is about 6 hours or more. In some embodiments, the blending time is about 8 hours or more. In some embodiments, the blending time is about 10 hours or more. In some embodiments, the blending time is about 12 hours or more.

In some embodiments, a pressure of up to 36,000 psi is utilized to generate a pellet. In some embodiments, the pressure is up to 34,000 psi. In some embodiments, the pressure is up to 32,000 psi. In some embodiments, the pressure is up to 30,000 psi. In some embodiments, the pressure is up to 28,000 psi. In some embodiments, the pressure is up to 26,000 psi. In some embodiments, the pressure is up to 24,000 psi. In some embodiments, the pressure is up to 22,000 psi. In some embodiments, the pressure is up to 20,000 psi. In some embodiments, the pressure is up to 18,000 psi. In some embodiments, the pressure is up to 16,000 psi. In some embodiments, the pressure is up to 15,000 psi. In some embodiments, the pressure is up to 14,000 psi. In some embodiments, the pressure is up to 10,000 psi.

In some embodiments, the pellets are compressed using a hydraulic press. In some embodiments, the powder is compressed under a 1-20 ton load. In some embodiments, the powder is compressed under a 2-18 ton load. In some embodiments, the powder is compressed under a 4-16 ton load. In some embodiments, the powder is compressed under a 6-14 ton load. In some embodiments, the powder is compressed under a 8-12 ton load. In some embodiments, the powder is compressed under a 9-11 ton load.

In some embodiments, the pellets are compressed using a hydraulic press. In some embodiments, the powder is compressed under a 1 ton load. In some embodiments, the powder is compressed under a 2 ton load. In some embodiments, the powder is compressed under a 3 ton load. In some embodiments, the powder is compressed under a 4 ton load. In some embodiments, the powder is compressed under a 5 ton load. In some embodiments, the powder is compressed under a 6 ton load. In some embodiments, the powder is compressed under a 7 ton load. In some embodiments, the powder is compressed under an 8 ton load. In some embodiments, the powder is compressed under a 9 ton load. In some embodiments, the powder is compressed under a 10 ton load. In some embodiments, the powder is compressed under a 11 ton load. In some embodiments, the powder is compressed under a 12 ton load. In some embodiments, the powder is compressed under a 13 ton load. In some embodiments, the powder is compressed under a 14 ton load. In some embodiments, the powder is compressed under a 15 ton load. In some embodiments, the powder is compressed under a 20 ton load.

In some embodiments, the metal and boron are compressed into a form that is not a pellet.

In some embodiments, a method described herein further comprises a sintering step. In some embodiments, the sintering step generates a densified composite matrix. In some embodiments, the sintering step is carried out at elevated temperatures. In some embodiments, the temperature during sintering is from 1000° C. to 2000° C. In some embodiments, the temperature during sintering is from 1000° C. to 1900° C. In some embodiments, the temperature during sintering is from 1200° C. to 1900° C. In some embodiments, the temperature during sintering is from 1300° C. to 1900° C. In some embodiments, the temperature during sintering is from 1400° C. to 1900° C. In some embodiments, the temperature during sintering is from 1000° C. to 1800° C. In some embodiments, the temperature during sintering is from 1000° C. to 1700° C. In some embodiments, the temperature during sintering is from 1200° C. to 1800° C. In some embodiments, the temperature during sintering is from 1300° C. to 1700° C. In some embodiments, the temperature during sintering is from 1000° C. to 1600° C. In some embodiments, the temperature during sintering is from 1500° C. to 1800° C. In some embodiments, the temperature during sintering is from 1500° C. to 1700° C. In some embodiments, the temperature during sintering is from 1500° C. to 1600° C. In some embodiments, the temperature during sintering is from 1600° C. to 2000° C. In some embodiments, the temperature during sintering is from 1600° C. to 1900° C. In some embodiments, the temperature during sintering is from 1600° C. to 1800° C. In some embodiments, the temperature during sintering is from 1600° C. to 1700° C. In some embodiments, the temperature during sintering is from 1700° C. to 2000° C. In some embodiments, the temperature during sintering is from 1700° C. to 1900° C. In some embodiments, the temperature during sintering is from 1700° C. to 1800° C. In some embodiments, the temperature during sintering is from 1800° C. to 2000° C. In some embodiments, the temperature during sintering is from 1800° C. to 1900° C. In some embodiments, the temperature during sintering is from 1900° C. to 2000° C.

In some embodiments, the temperature is about 1000° C., about 1100° C., about 1200° C., about 1300° C., about 1400° C., about 1500° C., about 1600° C., about 1700° C., about 1800° C., about 1900° C. or about 2000° C. In some embodiments, the temperature is about 1000° C. In some embodiments, the temperature is about 1100° C. In some embodiments, the temperature is about 1200° C. In some embodiments, the temperature is about 1300° C. In some embodiments, the temperature is about 1400° C. In some embodiments, the temperature is about 1500° C. In some embodiments, the temperature is about 1600° C. In some embodiments, the temperature is about 1700° C. In some embodiments, the temperature is about 1800° C. In some embodiments, the temperature is about 1900° C. In some embodiments, the temperature is about 2000° C.

In some embodiments, sintering is carried out using by electrical current. In some embodiments, sintering is carried out by arc-melting. In some embodiments, arc melting is carried out with a current (I) of 50 Amps (A) or more. In some embodiments, arc melting is carried out with a I of 60 A or more. In some embodiments, arc melting is carried out with a I of 65 A or more. In some embodiments, arc melting is carried out with a I of 70 A or more. In some embodiments, arc melting is carried out with a I of 75 A or more. In some embodiments, arc melting is carried out with a I of 80 A or more. In some embodiments, arc melting is carried out with a I of 90 A or more. In some embodiments, arc melting is carried out with a I of 100 A or more.

In some embodiments, arc melting is performed in and argon atmosphere. In some embodiments, arc melting is performed in an ultrapure argon atmosphere.

In some embodiments, arc melting is performed for 0.01-10 mins. In some embodiments, arc melting is performed for 0.01-8 mins. In some embodiments, arc melting is performed for 0.01-6 mins. In some embodiments, arc melting is performed for 0.01-5 mins. In some embodiments, arc melting is performed for 0.01-4 mins. In some embodiments, arc melting is performed for 0.5-3 mins. In some embodiments, arc melting is performed for 0.8-2.5 mins. In some embodiments, arc melting is performed for 1-2 mins.

In some embodiments, sintering is carried out at room temperature.

In some embodiment, a sintering step described herein involves an elevated temperature and an elevated pressure, e.g., hot pressing. Hot pressing is a process involving a simultaneous application of pressure and high temperature, which can accelerate the rate of densification of a material (e.g., a composite matrix described herein). In some embodiments, a temperature from 1000° C. to 2000° C. and a pressure of up to 36,000 psi are used during hot pressing.

In other embodiments, a sintering step described herein involves an elevated pressure and room temperature, e.g., cold pressing. In such embodiments, pressure of up to 36,000 psi is used.

Tools and Abrasive Materials

In some embodiments, a composite matrix described herein is used to make, modify, or coat a tool or an abrasive material. In some embodiments, a composite matrix described herein is coated onto the surface of a tool or an abrasive material. In some embodiments, the surface of a tool or an abrasive material is modified with a composite matrix described herein. In some embodiments, the surface of a tool or abrasive material comprises a composite matrix described herein.

In some embodiments, a tool or abrasive material comprises a cutting tool. In some embodiments, a tool or abrasive material comprises a tool or a component of a tool for cutting, drilling, etching, engraving, grinding, carving, or polishing. In some embodiments, a tool or abrasive material comprises a metal bond abrasive tool, for example, such as a metal bond abrasive wheel or grinding wheel. In some embodiments, a tool or abrasive material comprises drilling tools. In some embodiments, a tool or abrasive material comprises drill bits, inserts or dies. In some embodiments, a tool or abrasive material comprises tools or components used in downhole tooling. In some embodiments, a tool or abrasive material comprises an etching tool. In some embodiments, a tool or abrasive material comprises an engraving tool. In some embodiments, a tool or abrasive material comprises a grinding tool. In some embodiments, a tool or abrasive material comprises a carving tool. In some embodiments, a tool or abrasive material comprises a polishing tool.

Certain Terminologies

Unless defined otherwise, all technical and scientific terms used herein have the same meaning as is commonly understood by one of skill in the art to which the claimed subject matter belongs. It is to be understood that the detailed description are exemplary and explanatory only and are not restrictive of any subject matter claimed. In this application, the use of the singular includes the plural unless specifically stated otherwise. It must be noted that, as used in the specification, the singular forms “a,” “an” and “the” include plural referents unless the context clearly dictates otherwise. In this application, the use of “or” means “and/or” unless stated otherwise. Furthermore, use of the term “including” as well as other forms, such as “include”, “includes,” and “included,” is not limiting.

Although various features of the disclosure may be described in the context of a single embodiment, the features may also be provided separately or in any suitable combination. Conversely, although the disclosure may be described herein in the context of separate embodiments for clarity, the disclosure may also be implemented in a single embodiment.

Reference in the specification to “some embodiments”, “an embodiment”, “one embodiment” “another embodiment” or “other embodiments” means that a particular feature, structure, or characteristic described in connection with the embodiments is included in at least some embodiments, but not necessarily all embodiments, of the disclosure.

As used herein, ranges and amounts can be expressed as “about” a particular value or range. About also includes the exact amount. Hence “about 5 GPa” means “about 5 GPa” and also “5 GPa.” Generally, the term “about” includes an amount that would be expected to be within experimental error, e.g., ±5%, ±10% or ±15%. In some embodiments, “about” includes ±5%. In some embodiments, “about” includes ±10%. In some embodiments, “about” includes ±15%.

The section headings used herein are for organizational purposes only and are not to be construed as limiting the subject matter described.

EXAMPLES

These examples are provided for illustrative purposes only and not to limit the scope of the claims provided herein.

Example 1 X-Ray Diffraction

Prepared ingots were bisected using a diamond saw (Ameritool Inc., U.S.A.). One half was crushed into a sub 325 (45 μm) mesh powder and used for powder X-ray diffraction (PXRD) analysis; the other half was used for energy-dispersive X-ray spectroscopy (EDS) analysis and Vicker's hardness measurements. For the latter two, the samples were encapsulated in epoxy using an epoxy/hardener set (Allied High Tech Products Inc., U.S.A.). In order to achieve an optically flat surface, the samples were polished on a semi-automated polisher (South Bay Technology Inc., U.S.A.), using the following abrasives: SiC discs of 120-1200 grit sizes (Allied High Tech Products Inc., U.S.A.) and 30-1 micron particle diamond films (South Bay Technology Inc., U.S.A.).

Powder XRD was carried out on a Bruker D8 Discover Powder X-ray Diffractometer (Bruker Corporation, Germany) utilizing Cu_(Kα) X-ray radiation (λ=1.5418 Å). The following scan parameters were used: 5-100° 2 θ range, time per step of 0.3 sec, step size of 0.0353° with a scan speed of 0.1055°/sec. In order to determine the phases present in the powder X-ray diffraction data, the Joint Committee on Powder Diffraction Standards (JCPDS) database was utilized. The composition and purity of the samples were determined on an FEI Nova 230 high resolution scanning electron microscope (FEI Company, U.S.A.) with an UltraDry EDS detector (Thermo Scientific, U.S.A.). Rietveld refinement utilizing Maud software was carried out to determine the cell parameters.

ZrB₁₂, YB₁₂ and ScB₁₂ are completely soluble in each other. Zr_(1-x)Sc_(x)B₁₂ and Y_(1-x)Sc_(x)B₁₂ undergo a solid-state phase transition between a cubic and tetragonal cells at 90-95 at % Sc.

Table 1 shows unit cell data for Zr_(1-x)Y_(x)B₁₂. X-ray powder diffractograms of Zr_(1-x)Y_(x)B₁₂ are shown in FIG. 1.

TABLE 1 Concentration of Y in ZrB₁₂ Cubic (Fm3m) Compound (at. % Y)^(a) a (Å)^(b) a (Å)^(c) ZrB₁₂ — 7.412 (2) 7.412 Zr_(0.95)Y_(0.05)B₁₂  2.91 (0.10) 7.418 (3) 7.417 Zr_(0.75)Y_(0.25)B₁₂ 20.29 (0.12) 7.438 (4) 7.435 Zr_(0.50)Y_(0.50)B₁₂ 47.81 (0.55) 7.454 (3) 7.459 Zr_(0.25)Y_(0.75)B₁₂ 70.89 (0.46) 7.481 (6) 7.482 Zr_(0.05)Y_(0.95)B₁₂ 91.24 (0.41) 7.502 (3) 7.500 YB₁₂ — 7.505 (4) 7.505 ^(a)calculated from EDS analysis; errors are given in brackets ^(b)from cell refinement using Maud; errors are given in brackets ^(c)calculated using Vegard's Law

Table 2 shows unit cell data for Zr_(1-x)Sc_(x)B₁₂. X-ray powder diffractograms of Zr_(1-x)Sc_(x)B₁₂ are shown in FIG. 2.

TABLE 2 Concentration of Sc in ZrB₁₂ Cubic (Fm3m) Tetragonal (I4/mmm) Compound (at. % Sc)^(a) a (Å)^(b) a (Å)^(b) c (Å)^(b) ZrB₁₂ — 7.412 (2) — — Zr_(0.95)Sc_(0.05)B₁₂  2.20 (0.09) 7.412 (4) 5.241 (2) 7.411 (3) Zr_(0.75)Sc_(0.25)B₁₂ 15.14 (0.16) 7.410 (3) 5.240 (3) 7.410 (4) Zr_(0.50)Sc_(0.50)B₁₂ 38.66 (0.28) 7.408 (3) 5.237 (4) 7.408 (5) Zr_(0.25)Sc_(0.75)B₁₂ 65.16 (0.39) 7.405 (4) 5.235 (2) 7.405 (4) Zr_(0.20)Sc_(0.80)B₁₂ 67.49 (0.26) 7.403 (2) 5.234 (5) 7.402 (3) Zr_(0.15)Sc_(0.85)B₁₂ 87.17 (0.33) 7.402 (5) 5.233 (3) 7.393 (3) Zr_(0.10)Sc_(0.90)B₁₂ 90.51 (0.69) 7.398 (3) 5.233 (4) 7.389 (4) Zr_(0.05)Sc_(0.95)B₁₂ 94.97 (0.44) 7.395 (3) 5.232 (3) 7.385 (3) ScB₁₂ — — 5.232 (3) 7.361 (4) ^(a)calculated from EDS analysis; errors are given in brackets ^(b)from cell refinement using Maud; errors are given in brackets

Table 3 shows unit cell data for Y_(1-x)Sc_(x)B₁₂. X-ray powder diffractograms of Y_(1-x)Sc_(x)B₁₂ are shown in FIG. 3.

TABLE 3 Concentration Tetragonal of Sc in YB₁₂ Cubic (Fm3m) (I4/mmm) Compound (at. % Sc)^(a) a (Å)^(b) a (Å)^(b) c (Å)^(b) YB₁₂ — 7.505(4) — — Y_(0.95)Sc_(0.05)B₁₂  4.36 (0.17) 7.504 (3) 5.306 (2) 7.503 (3) Y_(0.75)Sc_(0.25)B₁₂ 26.45 (0.22) 7.486 (2) 5.292 (3) 7.486 (2) Y_(0.50)Sc_(0.50)B₁₂ 40.57 (0.28) 7.486 (2) 5.291 (4) 7.486 (3) Y_(0.25)Sc_(0.75)B₁₂ 65.79 (0.23) 7.455 (3) 5.272 (2) 7.452 (4) Y_(0.20)Sc_(0.80)B₁₂ 67.40 (0.31) 7.448 (4) 5.255 (5) 7.449 (5) Y_(0.15)Sc_(0.85)B₁₂ 73.90 (0.30) 7.442 (5) 5.247 (5) 7.439 (5) Y_(0.10)Sc_(0.90)B₁₂ 81.03 (0.39) 7.428 (6) 5.243 (3) 7.426 (6) Y_(0.05)Sc_(0.95)B₁₂ 92.38 (0.30) 7.402 (5) 5.235 (2) 7.389 (3) ScB₁₂ — — 5.232 (3) 7.361 (4) ^(a)calculated from EDS analysis; errors are given in brackets ^(b)from cell refinement using Maud; errors are given in brackets

Table 4 shows unit cell data for Zr_(1-x)Gd_(x)B₁₂. X-ray powder diffractograms of Zr_(1-x)Gd_(x)B₁₂ are shown in FIG. 4.

TABLE 4 Concentration of Gd in ZB₁₂ Cubic (at % Gd) by (Fm3m) Compound EDS α, Å Vegard's Law ZrB₁₂ — 7.412(2) 7.412 Zr_(0.95)Gd_(0.05)B₁₂  3.38 (0.23) 7.420(3) 7.418 Zr_(0.75)Gd_(0.25)B₁₂ 18.56 (0.31) 7.444(3) 7.440 Zr_(0.50)Gd_(0.50)B₁₂ 50.83 (0.80) 7.464(2) 7.468 Zr_(0.45)Gd_(0.55)B₁₂ 53.70 (0.64) 7.468(2) 7.474 Zr_(0.35)Gd_(0.65)B₁₂ — 7.453(2) 7.485 Zr_(0.25)Gd_(0.75)B₁₂ — — 7.496 Zr_(0.05)Gd_(0.95)B₁₂ — — 7.518 GdB₁₂ — 7.524 7.524

Table 5 shows unit cell data for Zr_(1-x)Sm_(x)B₁₂. X-ray powder diffractograms of Zr_(1-x)Sm_(x)B₁₂ are shown in FIG. 5.

TABLE 5 Concentration of Sm in ZB₁₂ Cubic (at % Sm) by (Fm3m) Compound EDS α, Å ZrB₁₂ — 7.412(2) Zr_(0.95)Sm_(0.05)B₁₂  2.93 (0.42) 7.419(3) Zr_(0.75)Sm_(0.25)B₁₂ 14.94 (0.24) 7.433(3) Zr_(0.70)Sm_(0.30)B₁₂ 13.99 (0.23) 7.431(4) Zr_(0.65)Sm_(0.35)B₁₂ — 7.429(2) Zr_(0.50)Sm_(0.50)B₁₂ — 7.428(3) SmB₁₂ — 7.543

Table 6 shows unit cell data for Zr_(1-x)Nd_(x)B₁₂. X-ray powder diffractograms of Zr_(1-x)Nd_(x)B₁₂ are shown in FIG. 6.

TABLE 6 Concentration of Nd in ZB₁₂ Cubic (at % Nd) by (Fm3m) Compound EDS a, Å ZrB₁₂ — 7.412 (2) Zr_(0.95)Nd_(0.05)B₁₂ 1.76 (0.11) 7.413 (3) Zr_(0.75)Nd_(0.25)B₁₂ 7.17 (0.28) 7.421 (2) Zr_(0.50)Nd_(0.50)B₁₂ — 7.419 (3)

Table 7 shows unit cell data for Zr_(1-x)Pr_(x)B₁₂. X-ray powder diffractograms of Zr_(1-x)Pr_(x)B₁₂ are shown in FIG. 7.

TABLE 7 Concentration of Pr in ZB₁₂ Cubic (at % Pr) by (Fm3m) Compound EDS a, Å ZrB₁₂ — 7.412 (2) Zr_(0.95)Pr_(0.05)B₁₂ 1.61 (0.22) 7.415 (2) Zr_(0.75)Pr_(0.25)B₁₂ 4.12 (0.27) 7.418 (4) Zr_(0.50)Pr_(0.50)B₁₂ — 7.418 (3)

058086.434938

The solubility limit of Gd in ZrB₁₂ is 54 at. % Gd. The solubility limit of Sm in ZrB₁₂ is ˜15 at. % Sm. The solubility limit of Pr in ZrB₁₂ is 4 at. % Pr. The solubility limit of Nd in ZrB₁₂ is ˜7 at. % Nd. With increasing concentration of Gd, Sm, Nd and Pr, the dodecaboride (MB₁₂) phase concentration decreases while the hexaboride (MB₆) phase increases. In most cases, the higher boride phases ZrB₅₀, GdB₆₆, SmB₆₆ or NdB₆₆ can be observed in the XRPD diffractograms as they accompany the dodecaboride phases at higher metal to boron ratios (1:20).

Table 8 shows the hkl, 2Theta and intensity values for a cubic dodecaboride alloy of the formula Zr_(1-x)Y_(x)B₁₂. X-ray powder diffractograms of Zr_(1-x)Y_(x)B₁₂ are shown in FIG. 1.

TABLE 8 Zr_(0.95)Y_(0.05)B₁₂ Zr_(0.75)Y_(0.25)B₁₂ Zr_(0.50)Y_(0.50)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.7026 65.05 20.6860 37.89 20.6081 69.57 2 2 0 0 23.9694 64.27 23.9341 54.40 23.8622 77.51 3 2 2 0 34.1433 21.65 34.0958 24.04 34.0068 27.27 4 3 1 1 40.2907 100.00 40.2119 100.00 40.0759 100.00 5 2 2 2 42.1499 26.40 42.0686 19.27 41.9283 23.75 6 4 0 0 49.0685 7.41 48.9665 6.47 48.8023 8.91 7 3 3 1 53.8300 24.41 53.6957 22.82 53.5130 16.60 8 4 2 0 55.3357 13.16 55.2003 7.92 55.0155 12.68 9 4 2 2 61.1600 24.42 61.0321 17.54 60.7954 22.83 10 5 1 1 65.3232 7.13 65.1830 6.34 64.9327 7.28 11 4 4 0 72.0237 1.56 71.8198 1.38 71.6078 2.42 12 5 3 1 75.8257 24.75 75.6271 18.14 75.5588 19.34 13 4 4 2 76.0645 13.42 76.9139 10.46 75.5950 13.97 14 6 2 0 77.0849 12.89 77.0707 7.95 76.8519 10.56 15 5 3 3 82.1129 4.88 81.8678 3.52 81.7783 5.01 16 6 2 2 85.8314 3.67 85.5586 2.30 86.6318 1.18 Zr_(0.25)Y_(0.75)B₁₂ Zr_(0.05)Y_(0.95)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%)  1 1 1 1 20.5293 89.17 20.5005 54.05  2 2 0 0 23.7543 78.40 23.6942 57.73  3 2 2 0 33.8576 35.08 33.7629 24.24  4 3 1 1 39.9183 100.00 39.8357 100.00  5 2 2 2 41.7846 32.82 41.6885 26.07  6 4 0 0 48.6299 8.44 48.5042 7.22  7 3 3 1 53.3210 28.35 53.1733 22.49  8 4 2 0 54.8221 17.32 54.6886 12.24  9 4 2 2 60.5763 26.41 60.4185 19.78 10 5 1 1 64.6989 15.25 64.4951 6.53 11 4 4 0 71.2255 3.49 71.0455 2.07 12 5 3 1 75.0477 20.23 74.8398 17.22 13 4 4 2 76.3177 18.68 76.0826 11.69 14 6 2 0 81.2397 6.12 81.0299 4.42 15 5 3 3 84.9269 5.11 84.6614 5.16 16 6 2 2 86.1455 2.02 85.8526 2.00

Table 9 shows the hkl, 2Theta and intensity values for a cubic dodecaboride alloy of the formula Zr_(1-x)Scxl312. X-ray powder diffractograms of Zr_(1-x)Sc_(x)B₁₂ are shown in FIG. 2.

TABLE 9 Zr_(0.95)Sc_(0.05)B₁₂ Zr_(0.75)Sc_(0.25)B₁₂ Zr_(0.50)Sc_(0.50)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.7178 58.46 20.7398 85.98 20.7361 57.70 2 2 0 0 23.9943 93.95 23.9757 85.23 23.9854 69.11 3 2 2 0 34.1912 31.37 34.1908 25.12 34.2016 24.02 4 3 1 1 40.3082 100.00 40.3168 100.00 40.3385 100.00 5 2 2 2 42.1836 22.92 42.1884 36.65 42.2354 26.93 6 4 0 0 49.1145 11.95 49.1069 9.17 49.1542 6.04 7 3 3 1 53.8591 23.18 53.8572 25.82 53.8745 14.22 8 4 2 0 55.3704 14.53 55.3652 13.17 55.3818 6.77 9 4 2 2 61.1900 27.28 61.1908 20.34 61.2867 15.71 10 5 1 1 65.4171 7.55 65.3704 6.57 65.4610 4.79 11 4 4 0 72.1084 2.43 72.1090 1.86 72.0250 0.89 12 5 3 1 75.8802 19.46 75.8806 26.93 75.8868 12.03 13 4 4 2 77.1615 18.47 77.1456 14.45 77.1449 7.27 14 6 2 0 77.3937 10.51 77.3910 7.38 82.0000 0.89 15 5 3 3 82.2883 3.16 82.1628 4.53 85.9550 1.06 16 6 2 2 85.9958 2.58 85.8891 3.36 87.4250 0.45 Zr_(0.25)Sc_(0.75)B₁₂ Zr_(0.20)Sc_(0.80)B₁₂ Zr_(0.15)Sc_(0.85)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.7626 44.77 20.7630 43.33 20.7648 48.83 2 2 0 0 24.0221 49.49 24.0289 68.73 24.0413 70.87 3 2 2 0 34.2209 16.61 34.2293 18.19 34.2271 16.89 4 3 1 1 40.3772 100.00 40.3784 100.00 40.3824 100.00 5 2 2 2 42.2572 25.52 42.2533 29.31 42.2827 37.10 6 4 0 0 49.3728 3.66 49.5156 3.62 49.4817 6.04 7 3 3 1 53.9280 18.53 53.9717 16.72 53.9719 20.02 8 4 2 0 55.4717 7.39 55.5050 31.28 55.5050 23.59 9 4 2 2 61.2527 14.18 61.3084 16.90 61.3268 20.89 10 5 1 1 65.1090 3.08 65.1321 2.84 65.0131 4.84 11 4 4 0 72.2350 1.38 72.0628 6.45 72.2350 18.08 12 5 3 1 75.9964 13.67 75.9738 12.33 75.9878 13.78 13 4 4 2 77.2635 9.98 77.3572 5.72 77.2838 10.53 14 6 2 0 82.5950 0.75 15 5 3 3 85.9833 2.19 16 6 2 2

Table 10 shows the hkl, 2Theta and intensity values for a tetragonal dodecaboride alloy of the formula X-ray poweder diffractograms of Zr_(1-x)Sc_(x)B₁₂ are shown in FIG. 2.

TABLE 10 Zr_(0.10)Sc_(0.90)B₁₂ Zr_(0.05)Sc_(0.95)B₁₂ No. h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 0 1 20.7899 29.49 20.7772 31.36 2 1 1 0 23.8350 44.55 23.8350 49.04 3 0 0 2 24.0564 54.16 24.0513 70.20 4 2 0 0 34.2377 11.90 33.9100 6.69 5 1 1 2 34.5400 7.24 34.2402 11.58 6 2 1 1 40.4064 100.00 40.3898 100.00 7 1 0 3 40.7377 10.13 40.7000 28.20 8 2 0 2 42.2998 23.22 42.2791 35.66 9 2 2 0 49.3360 6.21 49.3193 8.80 10 0 0 4 49.4133 14.18 49.6600 9.44 11 3 0 1 54.0191 15.30 53.6500 8.57 12 2 1 3 54.3280 12.89 54.0017 13.96 13 3 1 0 55.0850 10.11 55.2600 0.96 14 2 2 2 55.2961 8.18 55.5413 10.74 15 1 1 4 55.5050 12.19 56.0454 6.90 16 3 1 2 61.3601 16.07 61.3731 15.03 17 2 0 4 61.7989 7.05 61.8050 6.29 18 3 2 1 65.0957 4.68 65.2700 8.15 19 3 0 3 65.5681 12.43 65.7882 6.16

Table 11 shows the hkl, 2Theta and intensity values for a cubic dodecaboride alloy of the formula Y_(1-x)Sc_(x)B₁₂. X-ray powder diffractograms of Y_(1-x)Sc_(x)B₁₂ are shown in FIG. 3.

TABLE 11 Y_(0.95)Sc_(0.05)B₁₂ Y_(0.75)Sc_(0.25)B₁₂ Y_(0.50)Sc_(0.50)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.4964 58.91 20.5313 24.38 20.5203 57.33 2 2 0 0 23.6981 69.81 23.7549 28.92 23.7511 67.95 3 2 2 0 33.7648 26.79 33.8449 9.91 33.8601 23.15 4 3 1 1 39.8090 100.00 39.9113 52.32 39.9198 100.00 5 2 2 2 41.6500 31.96 41.8200 100.00 41.7777 30.08 6 4 0 0 48.4679 10.35 48.6098 3.31 48.6623 7.08 7 3 3 1 53.1722 22.19 53.3092 9.14 53.3144 20.98 8 4 2 0 54.6635 12.91 54.8020 4.65 54.8313 10.35 9 4 2 2 60.3876 22.63 60.5436 9.69 60.6240 17.76 10 5 1 1 64.4640 8.20 64.6994 2.10 64.7165 6.65 11 4 4 0 71.0483 3.13 71.2645 0.94 71.2974 2.12 12 5 3 1 74.7960 20.36 75.0107 8.10 75.0668 17.48 13 4 4 2 76.0474 14.68 76.2729 6.06 76.3554 10.94 14 6 2 0 80.9737 4.60 81.3056 1.28 81.2300 5.22 15 5 3 3 84.6176 3.89 84.8937 0.74 85.0192 2.50 16 6 2 2 85.8930 1.54 Zr_(0.25)Sc_(0.75)B₁₂ Zr_(0.20)Sc_(0.80)B₁₂ Zr_(0.15)Sc_(0.85)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.6260 36.04 20.6223 43.59 20.6693 46.39 2 2 0 0 23.8742 59.79 23.8791 73.79 23.8890 76.43 3 2 2 0 34.0158 13.77 34.0136 16.58 34.0796 13.94 4 3 1 1 40.0964 100.00 40.0985 100.00 40.1674 100.00 5 2 2 2 41.9741 21.08 41.9675 30.89 42.0556 31.36 6 4 0 0 48.8722 6.71 48.8909 7.82 48.9411 7.33 7 3 3 1 53.5244 13.88 53.5698 17.62 53.6881 12.43 8 4 2 0 55.0798 8.18 55.0734 7.11 55.1616 5.71 9 4 2 2 60.8667 16.75 60.8407 18.16 60.9368 17.02 10 5 1 1 64.9627 4.05 64.8644 4.90 65.0012 3.82 11 4 4 0 71.5700 1.42 71.5206 5.16 71.5700 1.17 12 5 3 1 75.4180 14.93 75.3873 11.57 75.5552 12.63 13 4 4 2 76.6782 12.64 76.6810 11.11 76.8241 12.74 14 6 2 0 81.4400 0.69 81.5800 1.52 15 5 3 3 85.2900 1.02 85.3950 2.11 16 6 2 2

Table₁₂ shows the hkl, 2Theta and intensity values for a tetragonal dodecaboride alloy of the formula Y_(1-x)Sc_(x)B₁₂. X-ray powder diffractograms of Y_(1-x)Sc_(x)B₁₂ are shown in FIG. 3.

TABLE 12 Y_(0.10)Sc_(0.90)B₁₂ Y_(0.05)Sc_(0.95)B₁₂ No. h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 0 1 20.6812 41.26 20.7148 41.80 2 1 1 0 23.5581 11.32 23.9050 81.86 3 0 0 2 23.9516 55.72 24.2200 37.24 4 2 0 0 33.7700 5.68 33.8900 8.78 5 1 1 2 34.1744 11.65 34.1939 20.50 6 2 1 1 40.2395 100.00 40.3298 100.00 7 1 0 3 40.5600 21.25 40.6726 17.35 8 2 0 2 42.1047 32.41 42.2141 42.34 9 2 2 0 49.0650 15.93 49.1700 28.96 10 0 0 4 49.4813 13.99 49.4740 24.64 11 3 0 1 52.9850 12.70 53.9185 15.60 12 2 1 3 53.7835 16.46 54.3885 22.43 13 3 1 0 54.7227 6.22 55.3699 13.83 14 2 2 2 55.2600 11.79 55.7155 10.26 15 1 1 4 55.6966 5.79 55.8742 11.52 16 3 1 2 61.0459 18.75 61.2640 16.93 17 2 0 4 61.4550 10.68 61.3500 31.17 18 3 2 1 64.9498 4.16 65.2267 11.14 19 3 0 3 65.3774 8.52 65.5369 14.65

Table 13 shows the hkl, 2Theta and intensity values for a cubic dodecaboride alloy of the formula Zr_(1-x)Gd_(x)B₁₂. X-ray powder diffractograms of Zr_(1-x)Gd_(x)B₁₂ are shown in FIG. 4.

TABLE 13 Zr_(0.95)Gd_(0.05)B₁₂ Zr_(0.75)Gd_(0.25)B₁₂ Zr_(0.50)Gd_(0.50)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.7399 95.93 20.6788 87.10 20.6085 93.87 2 2 0 0 24.0003 85.05 23.9010 73.41 23.8416 83.62 3 2 2 0 34.1848 29.59 34.0788 32.10 33.9797 41.84 4 3 1 1 40.3161 100.00 40.1971 100.00 40.0610 100.00 5 2 2 2 42.1798 35.81 42.0875 31.49 41.9272 43.00 6 4 0 0 49.1039 10.79 48.9955 7.29 48.7397 11.55 7 3 3 1 53.8340 20.77 53.6851 26.60 53.5045 23.29 8 4 2 0 55.3630 11.94 55.2286 13.31 55.0078 13.05 9 4 2 2 61.1759 22.15 61.0029 23.17 60.7900 34.39 10 5 1 1 65.3611 8.13 65.1884 10.34 64.9650 7.17 11 4 4 0 72.0117 2.51 71.7155 9.94 71.4914 13.80 12 5 3 1 75.8327 14.63 75.5956 16.24 75.3063 28.32 13 4 4 2 76.0695 7.55 76.8649 13.25 76.5720 23.79 14 6 2 0 77.1034 12.00 77.0441 12.19 81.5100 5.09 15 5 3 3 82.1064 2.63 81.8641 2.97 85.1850 4.84 16 6 2 2 85.8590 2.35 85.6050 1.97 86.5150 2.00 Zr_(0.55)Gd_(0.45)B₁₂ Zr_(0.65)Gd_(0.35)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.6071 83.86 20.6387 100.00 2 2 0 0 23.8274 100.00 23.8697 65.41 3 2 2 0 33.9574 42.05 34.0230 38.09 4 3 1 1 40.0382 95.84 40.1173 97.72 5 2 2 2 41.8981 24.82 42.0336 32.66 6 4 0 0 48.8118 9.80 53.6360 19.07 7 3 3 1 53.4668 26.08 54.6538 72.77 8 4 2 0 54.9771 18.14 60.8403 22.59 9 4 2 2 60.7139 21.08 65.2000 35.84 10  5 1 1 64.8691 10.12 71.6913 36.39 11  4 4 0 71.6400 14.96 75.4766 15.27 12  5 3 1 75.2413 28.80 76.7779 15.57 13  4 4 2 76.4965 21.71 14  6 2 0 81.6850 4.64 15  5 3 3 16  6 2 2

Table 14 shows the hkl, 2Theta and intensity values for a cubic dodecaboride alloy of the formula Zr_(1-x)Sm_(x)B₁₂. X-ray powder diffractograms of Zr_(1-x)Sm_(x)B₁₂ are shown in FIG. 5.

TABLE 14 Zr_(0.95)Sm_(0.05)B₁₂ Zr_(0.75)Sm_(0.25)B₁₂ Zr_(0.70)Sm_(0.30)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.7436 85.19 20.7049 87.59 20.7140 76.55 2 2 0 0 23.9854 77.80 23.9708 72.65 23.9607 84.46 3 2 2 0 34.1869 31.82 34.1242 32.90 34.1286 23.74 4 3 1 1 40.3040 100.00 40.2444 100.00 40.2499 100.00 5 2 2 2 42.1811 34.25 42.1192 32.38 42.1361 26.58 6 4 0 0 49.1089 9.97 49.2909 21.98 49.2748 27.84 7 3 3 1 53.8419 24.99 53.7459 35.20 53.7530 22.20 8 4 2 0 55.3619 13.12 55.2524 17.75 55.3325 12.38 9 4 2 2 61.1938 20.73 61.0529 22.71 61.1205 15.11 10 5 1 1 65.3383 8.49 65.2486 8.04 65.2905 6.50 11 4 4 0 72.0605 1.86 72.2724 11.71 72.2350 17.32 12 5 3 1 75.8377 19.15 75.6644 19.66 75.6771 17.62 13 4 4 2 77.1195 11.80 76.9350 12.94 76.9644 10.02 14 6 2 0 82.1043 2.24 81.7900 0.81 82.2450 1.85 15 5 3 3 85.9068 1.15 82.1400 1.39 16 6 2 2 87.1150 1.01 85.7309 2.37 Zr_(0.50)Sm_(0.50)B₁₂ # h k l 2Θ° I_(rel) (%)  1 1 1 1 20.7265 83.37  2 2 0 0 23.9744 90.90  3 2 2 0 34.1616 25.18  4 3 1 1 40.2558 92.10  5 2 2 2 42.1358 45.35  6 4 0 0 49.2995 100.00  7 3 3 1 53.7991 25.05  8 4 2 0 55.3094 16.46  9 4 2 2 61.1152 30.72 10 5 1 1 71.6165 14.78 11 4 4 0 75.6890 20.49 12 5 3 1 76.1900 21.82 13 4 4 2 14 6 2 0 15 5 3 3 16 6 2 2

Table 15 shows the hkl, 2Theta and intensity values for a cubic dodecaboride alloy of the formula Zr_(1-x)Nd_(x)B₁₂. X-ray powder diffractograms of Zr_(1-x)Nd_(x)B₁₂ are shown in FIG. 6.

TABLE 15 Zr_(0.95)Nd_(0.05)B₁₂ Zr_(0.75)Nd_(0.25)B₁₂ Zr_(0.50)Nd_(0.50)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.7586 74.00 20.7497 83.40 20.7456 72.77 2 2 0 0 24.0140 78.92 23.9956 87.59 24.0122 57.89 3 2 2 0 34.1997 29.66 34.1975 33.63 34.1936 28.35 4 3 1 1 40.3216 100.00 40.3224 100.00 40.3400 87.05 5 2 2 2 42.2093 29.42 42.1930 37.94 42.2002 27.22 6 4 0 0 49.1216 10.30 49.3062 31.64 49.3139 100.00 7 3 3 1 53.8682 28.24 53.8432 23.94 53.8959 19.68 8 4 2 0 55.3969 10.73 55.3794 12.80 55.4135 26.69 9 4 2 2 61.2063 20.87 61.1851 25.96 61.2281 14.60 10 5 1 1 65.3797 6.37 65.3465 7.93 65.3098 16.94 11 4 4 0 72.0496 3.01 71.7800 0.58 72.1300 22.45 12 5 3 1 75.8700 17.10 75.8255 19.07 76.0967 7.76 13 4 4 2 77.1479 9.71 77.0933 12.63 77.4150 2.87 14 6 2 0 82.2448 1.78 82.1980 2.20 15 5 3 3 85.8712 2.90 84.3800 0.53

Table 16 shows the hkl, 2Theta and intensity values for a cubic dodecaboride alloy of the formula Zr_(1-x)Pr_(x)B₁₂. X-ray powder diffractograms of Zr_(1-x)Pr_(x)B₁₂ are shown in FIG. 7.

TABLE 16 Zr_(0.95)Pr_(0.05)B₁₂ Zr_(0.75)Pr_(0.25)B₁₂ Zr_(0.50)Pr_(0.50)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.7375 92.84 20.7495 70.17 20.7476 64.31 2 2 0 0 24.0010 93.37 24.0094 72.41 24.0090 49.77 3 2 2 0 34.1815 25.89 34.2048 33.50 34.2222 17.60 4 3 1 1 40.3346 100.00 40.3362 100.00 40.3419 72.07 5 2 2 2 42.1989 37.76 42.2141 32.24 42.2263 29.16 6 4 0 0 49.1034 11.12 49.2052 31.88 49.2283 100.00 7 3 3 1 53.8531 31.81 53.8757 21.71 53.5800 1.12 8 4 2 0 55.3989 14.05 55.4408 10.53 55.7129 9.53 9 4 2 2 61.2026 23.30 61.2064 22.90 61.2131 13.05 10 5 1 1 65.3592 8.08 65.4264 4.81 65.4100 21.87 11 4 4 0 72.1605 2.68 72.1542 10.53 72.2167 24.70 12 5 3 1 75.8634 22.19 75.8540 14.84 75.8402 18.39 13 4 4 2 77.1447 16.97 77.1039 8.19 77.2670 15.13 14 6 2 0 82.4289 1.84 82.0000 0.95 82.3500 1.49 15 5 3 3 85.8500 2.39

Table 17 shows the hkl, 2Theta and intensity values for a cubic dodecaboride alloy of the formula Zr_(1-x)Y_(x)B₁₂ prepared using a metal to boron ratio of 1 to 13. X-ray powder diffractograms of Zr_(1-x)Y_(x)B₁₂ prepared using a metal to boron ratio of 1 to 13 shown in FIG. 14.

TABLE 17 Zr_(0.95)Y_(0.05)B₁₂ Zr_(0.75)Y_(0.25)B₁₂ Zr_(0.50)Y_(0.50)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.7355 73.46 20.7002 71.95 20.6212 69.98 2 2 0 0 23.9946 60.6 23.9456 65.33 23.8571 77.65 3 2 2 0 34.1996 28.06 34.1128 25.85 33.9807 27.32 4 3 1 1 40.3165 100 40.215 100 40.075 100 5 2 2 2 42.1942 28.85 42.0944 30.99 41.9376 32.52 6 4 0 0 49.1008 6.89 48.9676 6.71 48.8143 10.82 7 3 3 1 53.8424 27.08 53.7116 21.46 53.5215 25.2 8 4 2 0 55.3707 12.53 55.2221 12.41 55.0229 15.1 9 4 2 2 61.1854 26.71 61.0171 21.66 60.809 23.52 10 5 1 1 65.3368 8.26 65.1641 6.72 64.9404 9.71 11 4 4 0 72.0002 3.37 71.772 3.03 71.5162 2.87 12 5 3 1 75.8539 21.49 75.6176 18.01 75.3481 19.97 13 4 4 2 76.0955 11.12 75.8566 9.18 76.6094 15.09 14 6 2 0 77.1219 14.7 76.8815 12.12 81.5983 4.52 15 5 3 3 82.1404 4.03 81.8827 4.27 81.8414 2.29 16 6 2 2 85.871 2.66 85.6007 2.79 85.5583 1.55 Zr_(0.25)Y_(0.75)B₁₂ Zr_(0.05)Y_(0.95)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%)  1 1 1 1 20.5795 52.79 20.5188 61.69  2 2 0 0 23.8051 56.88 23.7555 65.07  3 2 2 0 33.9166 26.82 33.8219 29.93  4 3 1 1 39.9739 100 39.8751 100  5 2 2 2 41.8384 26.55 41.726 26.86  6 4 0 0 48.6771 6.93 48.5698 7.06  7 3 3 1 53.3717 19.66 53.2352 22.3  8 4 2 0 54.8634 13.03 54.7391 18.77  9 4 2 2 60.6127 18.23 60.4644 20.74 10 5 1 1 64.7274 6.11 64.5777 7.42 11 4 4 0 71.2913 2.97 71.1007 2.69 12 5 3 1 75.0889 16.1 74.8923 16.5 13 4 4 2 75.3243 8.28 76.1436 10.82 14 6 2 0 76.3386 10.86 76.3831 5.71 15 5 3 3 81.2894 3.03 81.0903 3.84 16 6 2 2 84.9457 2.19 84.7505 2.73

Example 2 Hardness Determination

The hardness of each sample was determined using a MicroMet 2103 Vickers microhardness tester (Buehler Ltd, U.S.A.). Fifteen indents of the following force loading were made in random areas of the sample: 0.49, 0.98, 1.96, 2.94 and 4.9 N (low to high, respectively). The length of the diagonals were measured using a high resolution optical microscope (Zeiss Axiotech 100HD, Carl Zeiss Vision GmbH, Germany) with 500× magnification, and Vickers hardness was calculated using Equation 1:

$\begin{matrix} {H_{v} = \frac{1854.4F}{a^{2}}} & (1) \end{matrix}$

where F is the loading force applied in Newton (N) and a is the average of the length of the two diagonals of each indent in micrometers.

Measurements of Vickers microindentation hardness of Zr_(1-x)Y_(x)B₁₂ are shown in FIG. 8.

Measurements of Vickers microindentation hardness of Zr_(1-x)Sc_(x)B₁₂ are shown in FIG. 9.

Measurements of Vickers microindentation hardness of Y_(1-x)Sc_(x)B₁₂ are shown in FIG. 10.

Measurements of Vickers microindentation hardness of Zr_(1-x)Gd_(x)B₁₂ are shown in FIG. 11.

Example 3 Oxidation Resistance

Oxidation resistance was determined via thermogravimetric analysis utilizing a Pyris Diamond TGA/DTA unit (TG-DTA, Perkin-Elmer Instruments, U.S.A.). The following heating/cooling profile was used: heating in air from 25 to 200° C. (at 20° C./min), holding at 200° C. for 30 minutes, heating from 200 to 1000° C. (at 2° C./min), holding at 1000° C. for 120 minutes, cooling 1000 to 25° C. (at 5° C./min).

FIG. 12 shows the thermal stability of pure ZrB₁₂, YB₁₂ and ScB₁₂ and the hardest solid solutions of mixed metal dodecaborides as measured by thermal gravimetric analysis in air. These data show that Zr_(0.5)Y_(0.5)B₁₂, Zr_(0.5)Sc_(0.5)B₁₂ and Y_(0.5)Sc_(0.5)B₁₂ are stable up to ˜630° C., ˜685° C. and ˜695 ° C., respectively (using the extrapolated oxidation onset), compared to ˜610° C. for pure ZrB₁₂, ˜715° C. for pure YB₁₂ and ˜685° C. pure ScB₁₂.

FIG. 13 shows the thermal stability of pure ZrB₁₂, Zr_(0.5)Gd_(0.5)B₁₂ and Zr_(0.75)Sm_(0.25)B₁₂ as measured by thermal gravimetric analysis in air. These data show that Zr_(0.5)Gd_(0.5)B₁₂ is stable up to ˜630° C., while Zr_(0.75)Sm_(0.25)B₁₂ up to ˜620° C., compared to ˜610° C. for pure ZrB₁₂.

Example 4 Preparation

Mixed dodecaboride solid solutions, Zr_(1-x)Y_(x)B₁₂, (x=0.00, 0.05, 0.25, 0.50, 0.75, 0.95 and 1.00), Zr_(1-y)Sc_(y)B₁₂, Y_(1-y)Sc_(y)B₁₂ (y=0.00, 0.05, 0.25, 0.50, 0.75, 0.80, 0.85, 0.90, 0.95 and 1.00), ScB₅₀and YB₆₆ were synthesized using metal and boron powders of high-purity: amorphous boron (99+%, Strem Chemicals, U.S.A.), zirconium (99.5%, Strem Chemicals, U.S.A.), yttrium (99.9%, Strem Chemicals, U.S.A.) and scandium (99.9%, Sigma-Aldrich, U.S.A.). In order to prevent the formation of the lower boride phases, a metals to boron ratio of 1:20 was used for the dodecaborides, 1:65 for ScB₅₀and 1:70 for YB₆₆. The powders of boron and transition metals were weighed, homogenized in an agate mortar and pestle and pressed into pellets using a hydraulic press (Carver) under a 10 ton load. The samples were then arc-melted (I≥70 amps, t=1-2 mins) in an ultra-high purity argon atmosphere.

Pellets of Zr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Pr_(x)B₁₂, and Zr_(1-x)Nd_(x)B₁₂ (x=0.05, 0.25, 0.50, 0.75, and 0.95) were prepared using high-purity metal and boron powders: amorphous boron (99+%, Strem Chemicals), gadolinium (99%, Sigma-Aldrich), zirconium (99.5%, Strem Chemicals), samarium (Strem Chemicals, 99.9%), praseodymium (99.9%, Strem Chemicals), and neodymium (99.8%, Strem Chemicals). The metal to boron ratio was kept at a minimum of 1:20 to prevent the formation of lower borides (MB₆) as they are the most stable boride phases of Gd, Sm, Nd, and Pr at ambient pressure. The weighed mixtures were homogenized in vials in a vortex mixer for ˜1 min, and then consolidated in a hydraulic press (Carver) under 10 tons before being arc melted (I>70 A, T=1-2 min) under a high purity argon atmosphere.

Example 5 Unit Cell Analysis

Metal dodecaborides (MB₁₂) constitute a class of boron rich compounds previously studied for their magnetic, optical and electronic properties. The structure of all dodecaborides contains boron cuboctahedron cages composed of 24 atoms, each containing a 12-coordinate metal in its center. The cages are usually arranged in a face-centered cubic close packed arrangement, forming the cubic-UB₁₂ (Fm3m) structure; however, ScB₁₂ forms its own structural type—tetragonal-ScB₁₂ (I4/mmm), where the cuboctahedra are arranged in a body-centered tetragonal close-packed structure.

FIG. 15 shows the unit cell of the cubic-UB₁₂ (top left) dodecaboride structure type: metal atoms are in blue, B atoms in yellow, (top right) cubic-UB₁₂ polyhedra model: face-centered cubic (FCC) lattice of 24 boron atom cuboctahedra boron cages surrounding₁₂-coordinate metal atoms; (bottom left) the unit cell of the tetragonal-ScB₁₂ dodecaboride structure type: metal atoms are in magenta, B atoms in yellow, (bottom right) tetragonal-ScB₁₂ polyhedra model: body-centered tetragonal (BCT) lattice of 24 boron atom cuboctahedra boron cages surrounding₁₂-coordinate metal atoms. Note, while 24 borons surround each metal atom, each metal atom is equidistant from 12 B-B bonds, making it₁₂-coordinate.

FIG. 16 shows the crystal structure of ScB₅₀, known as the β-rhombohedral boron doping phase of scandium (Inorganic Crystal Structure Database (ICSD) 2204, space group R3m), showing characteristic boron icosahedra; (right) crystal structure of YB₆₆ (ICSD 23186, space group Fm3c). (Boron atoms, which are part of B₁₂ clusters are shown as green icosahedra, other boron atoms are in dark red, scandium atoms are in violet, yttrium atoms are in teal).

FIG. 17 shows a polyhedra model of the unit cell of a cubic-UB₁₂ structural type metal dodecaboride (top left): 24 boron atom cuboctahedra cages (square faces shown in red, hexagonal face in green) are arranged in a FCC lattice, with a 12-coordinate metal atom in the center of each cage; (top right) polyhedra model of the unit cell of a tetragonal-ScB₁₂ structural type metal dodecaboride: 24 boron atom cuboctahedra cages (square faces shown in red, hexagonal facein green) are arranged in a BCT lattice, with a 12-coordinate metal atom in the center of each cage; Note, metals are considered 12-coordinate since 12 boron-boron bonds are equidistant from each metal atom in the 24 boron atom cuboctahedron cage; (bottom left) polyhedra model of the unit cell of a rhombohedral-MB₅₀ structural type (solid solution of a metal in β-rhombohedral boron): boron atoms are arranged in B₁₂ icosahedral units (shown in green), metal atoms are in blue; (bottom right) polyhedra model of the unit cell of a cubic-YB₆₆ structural type metal boride: boron atoms are arranged in B₁₂ icosahedral units (shown in green), boron atoms not forming icosahedra are in red, metal atoms are in blue.

Example 6 Energy Dispersive X-ray Analysis (EDS)

Elemental maps and SEM images of selected samples of Zr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Nd_(x)B₁₂ and Zr_(1-x)Pr_(x)B₁₂ alloys (x=0.55, 0.30, 0.25 and 0.25 respectively) are presented in FIG. 18. Elemental maps for boron (K line), zirconium (L line) and gadolinium, samarium, neodymium and praseodymium (L lines) of: (a) the Zr_(0.45)Gd_(0.55)B₁₂ solid solution showing the presence of zirconium and gadolinium in the dodecaboride phase. The boron rich areas correspond to a higher boride phase GdB₆₆ (cubic, Fm3c structure, a=23.449 Å, ICSD (Inorganic Crystal Structure Database) 614306); (b) the Zr_(0.70)Sm_(0.30)B₁₂ solid solution showing the presence of zirconium and samarium in the dodecaboride phase. The samarium rich areas correspond to SmB₆ (cubic, Pm3m structure, a=4.133 Å, ICSD 194196), while the boron rich areas correspond to a higher boride phase SmB₆₆ (cubic, Fm3c structure, a=23.468 Å). (c) the Zr_(0.75)Nd_(0.25)B₁₂ solid solution showing the presence of zirconium and neodymium in the dodecaboride phase. The neodymium rich areas correspond to NdB₆ (cubic, Pm3m structure, a=4.127 Å, ICSD 614931), while the boron rich areas correspond to a higher boride phase NdB₆₆ (cubic, Fm3c structure, a=23.476 Å) and ZrBso (rhombohedral, R3m structure, a=10.932 Å, c=23.849 Å); (d) the Zr_(0.75)Pr_(0.25)B₁₂ solid solution showing the presence of zirconium and praseodymium in the dodecaboride phase. The praseodymium rich areas correspond to PrB₆ (cubic, Pm3m structure, a=4.123 Å, ICSD 615183), while the boron rich areas correspond to a higher boride phase ZrBso (rhombohedral, R3m structure, a=10.932 Å, c=23.849 Å). The thick horizontal bars represent the intensity as a color legend.

FIG. 19 shows the SEM images and elemental maps for the hardest compositions of the mixed metal dodecaborides: Zr_(0.5)Y_(0.5)B₁₂, Zr_(0.5)Sc_(0.5)B₁₂ and Y_(0.5)Sc_(0.5)B₁₂. For Zr_(0.5)Y_(0.5)B₁₂, both Zr and Y can be observed in the metal dodecaboride phase. In contrast, for the Sc containing dodecaboride solid solutions, Zr_(0.5)Sc_(0.5)B₁₂ and Y_(0.5)Sc_(0.5)B₁₂, while Zr and Y can be seen primarily in the dodecaboride phase, Sc can be seen both in the dodecaboride phase as well as in boron rich areas (as ScB₅₀). SEM images and elemental maps for boron (K line), scandium (K line), yttrium (L line), zirconium (L line) for mixed metal dodecaboride solid-solutions: (top) Zr_(0.5)Y_(0.5)B₁₂, (middle) Zr_(0.5)Sc_(0.5)B₁₂, (bottom) Y_(0.5)Sc_(0.5)B₁₂. For Zr_(0.5)Y_(0.5)B₁₂ both zirconium and yttrium can be observed in the metal dodecaboride phase. In contrast, for the scandium containing dodecaboride solid solutions, Zr_(0.5)Sc_(0.5)B₁₂ and YO.5Sc_(0.5)B₁₂, while yttrium can be seen primarily in the dodecaboride phase, scandium can be seen both in dodecaboride phase as well as in boron rich areas (as ScB₅₀). The thick horizontal bars represent the intensity as a color legend.

Example 7 Optical Microscopy

FIG. 20 shows the colors of solid solution samples of the mixed metal dodecaborides taken using an optical microscope. A color change of the dodecaboride phase can be directly observed using a light microscope going from pure ZrB₁₂ (violet) to YB₁₂ (light-blue) and ScB₁₂ (iceberg blue) phase.The color change is most pronounced for the Zr_(1-x)Y_(x)B₁₂ solid solution, which goes from violet for ZrB₁₂ to light blue for YB₁₂. The color changes for Zr_(1-x)Sc_(x)B₁₂ and Y_(1-x)Sc_(x)B₁₂ are less pronounced due to the similarities of the shades of blue of YB₁₂ and ScB₁₂.

The solid solution formation of the dodecaboride phase can be directly observed using a light microscope going from pure ZrB₁₂ (violet) to Zr_(0.45)Gd_(0.55)B₁₂ (blue) and Zr_(0.70)Sm_(0.30)B₁₂ (blue-violet) shown in FIG. 21. The color change is due to the charge-transfer between the cuboctahedron boron cage network and the metal atoms. It also suggests that pure GdB₁₂ and SmB₁₂ should be blue, similar to YB₁₂, as Gd, Sm and Y are all in +3 oxidation states. The dark blue phase observed in Zr_(1-x)Sm_(x)B₁₂ is SmB₆.

EXPERIMENTAL

Zr_(1-x)Y_(x)B₁₂ Zr_(1-y)Sc_(y)B₁₂ and Y_(1-y)Sc_(y)B₁₂

Mixed dodecaboride solid solutions, Zr_(1-x)Y_(x)B₁₂, (x=0.00, 0.05, 0.25, 0.50, 0.75, 0.95 and 1.00), Zr_(1-y)Sc_(y)B₁₂, Y_(1-y)Sc_(y)B₁₂ (y=0.00, 0.05, 0.25, 0.50, 0.75, 0.80, 0.85, 0.90, 0.95 and 1.00), ScB₅₀ and YB₆₆ were synthesized using metal and boron powders of high-purity: amorphous boron (99+%, Strem Chemicals, U.S.A.), zirconium (99.5%, Strem Chemicals, U.S.A.), yttrium (99.9%, Strem Chemicals, U.S.A.) and scandium (99.9%, Sigma-Aldrich, U.S.A.). In order to prevent the formation of the lower boride phases, a metals to boron ratio of 1:20 was used for the dodecaborides, 1:65 for ScB₅₀ and 1:70 for YB₆₆. The powders of boron and transition metals were weighed, homogenized in an agate mortar and pestle and pressed into pellets using a hydraulic press (Carver) under a 10 ton load. The samples were then arc-melted (I≥70 amps, t=1-2 mins) in an ultra-high purity argon atmosphere.

Prepared ingots were bisected using a diamond saw (Ameritool Inc., U.S.A.). One half was crushed into a sub 325 (45 μm) mesh powder and used for powder X-ray diffraction (PXRD) analysis; the other half was used for energy-dispersive X-ray spectroscopy (EDS) analysis and Vicker's hardness measurements. For the latter two, the samples were encapsulated in epoxy using an epoxy/hardener set (Allied High Tech Products Inc., U.S.A.). In order to achieve an optically flat surface, the samples were polished on a semi-automated polisher (South Bay Technology Inc., U.S.A.), using the following abrasives: SiC discs of 120-1200 grit sizes (Allied High Tech Products Inc., U.S.A.) and 30-1 micron particle diamond films (South Bay Technology Inc., U.S.A.).

Powder XRD was carried out on a Bruker D8 Discover Powder X-ray Diffractometer (Bruker Corporation, Germany) utilizing Cu_(Kα) X-ray radiation (λ=1.5418 Å). The following scan parameters were used: 5-100° 2 θ range, time per step of 0.3 sec, step size of 0.0353° with a scan speed of 0.1055°/sec. In order to determine the phases present in the powder X-ray diffraction data, the Joint Committee on Powder Diffraction Standards (JCPDS) database was utilized. The composition and purity of the samples were determined on an FEI Nova 230 high resolution scanning electron microscope (FEI Company, U.S.A.) with an UltraDry EDS detector (Thermo Scientific, U.S.A.). Transmission electron microscopy (TEM) was performed on a TF-20 transmission electron microscope in order to confirm the crystal structure. Rietveld refinement utilizing Maud software was carried out to determine the cell parameters. The hardness of each sample was determined using a MicroMet 2103 Vickers microhardness tester (Buehler Ltd, U.S.A.). Fifteen indents of the following force loading were made in random areas of the sample: 0.49, 0.98, 1.96, 2.94 and 4.9 N (low to high, respectively). The length of the diagonals were measured using a high resolution optical microscope (Zeiss Axiotech 100HD, Carl Zeiss Vision GmbH, Germany) with 500× magnification, and Vickers hardness was calculated using the Equation below:

$H_{v} = \frac{1854.4F}{a^{2}}$

where F is the loading force applied in Newtons (N) and a is the average of the length of the two diagonals of each indent in micrometers.

Densities for the 50/50% solid solutions were calculated from powder XRD unit cell data and elemental composition from EDS.

Oxidation resistance was determined via thermogravimetric analysis utilizing a Pyris Diamond TGA/DTA unit (TG-DTA, Perkin-Elmer Instruments, U.S.A.). The following heating/cooling profile was used: heating in air from 25 to 200° C. (at 20° C./min), holding at 200° C. for 30 minutes, heating from 200 to 1000° C. (at 2° C./min), holding at 1000° C. for₁₂₀ minutes, cooling 1000 to 25° C. (at 5° C./min).

To determine and establish the composition and phase purity of mixed MB₁₂ solid solutions, powder X-ray diffraction (PXRD) and energy-dispersive X-ray spectroscopy (EDS) analyses were performed. FIGS. 1-3 show PXRD in the 5-100° 2 Θ for the three solid solutions: Zr_(1-x)Y_(x)B₁₂ (x=0.05, 0.25, 0.50, 0.75 and 0.95), Zr_(1-y)Sc_(y)B₁₂ and Y_(1-y)Sc_(y)B₁₂ (y=0.05, 0.25, 0.50, 0.75, 0.80, 0.85, 0.90 and 0.95). PXRD data for the β-rhombohedral boron doping phase of Sc (ScB₅₀, R3l m) and YB₆₆ (Fm3c) (FIG. 16) compared to the reference patterns from JCPDS (Joint Committee for Powder Diffraction Standards) can be seen in FIG. 24.

The three dodecaborides, ZrB₁₂, YB₁₂ and ScB₁₂, are completely soluble in each other as binary metal substituted phases: Zr_(1-x)Y_(x)B₁₂, Zr_(1-x)Sc_(x)B₁₂ and Y_(1-x)Sc_(x)B₁₂. Samples with YB₁₂ contain YB₆₆ as a minor phase, while ScB₁₂ samples contain ScBso (FIGS. 16 and 24). ZrB₁₂ and YB₁₂ form an essentially perfect solid solution (FIGS. 15 and Table 1), which follows Vegard's Law within experimental error. This can be attributed to the fact that both of these dodecaborides have the cubic-UB₁₂ (Fm3m) structure, the electronegativities of the metals are similar, and the differences in their radii are within the 15% set by the Vegard's Law rules. On the other hand, ScB₁₂ possesses a tetragonal-ScB₁₂ structure. This results in Zr_(1-x)Sc_(x)B₁₂ and Y_(1-x)Sc_(x)B₁₂ solid solutions having a solid-state phase transition at 90-95 at. % Sc (FIGS. 1-3 and Table 2-3). In addition, Zr_(1-x)Sc_(x)B₁₂ solid solutions were previously shown to undergo a temperature induced phase transition. Unit cell parameters for cubic (FCC) and body-centered tetragonal (BCT) syngonies as well as the phase composition as determined by EDS are presented in Tables 1-3. FIG. 19 shows the SEM images and elemental maps for the hardest compositions of the mixed metal dodecaborides: Zr_(0.5)Y_(0.5)B₁₂, Zr_(0.5)Sc_(0.5)B₁₂ and Y_(0.5)Sc_(0.5)B₁₂. For Zr_(0.5)Y_(0.5)B₁₂, both Zr and Y can be observed in the metal dodecaboride phase. In contrast, for the Sc containing dodecaboride solid solutions, Zr_(0.5)Sc_(0.5)B₁₂ and Y_(0.5)Sc_(0.5)B₁₂, while Zr and Y can be seen primarily in the dodecaboride phase, Sc can be seen both in the dodecaboride phase as well as in boron rich areas (as ScB₅₀).

After establishing the purity of the samples, Vickers hardness testing (under a load of 0.49-4.9 N) was carried out, the results of which are shown in FIGS. 8-10. High covalent bond density of the dodecaborides may be the reason that both pure MB₁₂ as well as their mixed metal solid solutions are superhard (FL >40 GPa). For the Zr_(1-x)Y_(x)B₁₂ solid solution, at the composition of Y=50 at. %, the hardness maximizes at 45.8 ±1.3 GPa for a loading of 0.49 N, compared to 40.4±1.8 GPa for pure ZrB₁₂ (compared to a literature value of 39 GPa) and 40.9±1.6 GPa for pure YB₁₂ (compared to a literature value of 42 GPa). We speculate that the 14% increase in hardness here is due to a combination of both intrinsic factors (solid solution hardening) where incorporating atoms of different sizes (Zr: r_(at)=1.55 Å, r_(CN=12)=1.603 Å; Y: r_(at)=1.80 Å, r_(CN=12)=1.801 Å) produces strain at a local scale and dislocation propagation is therefore hindered; as well as extrinsic factors (due to sample morphology, microstructure and the presence of boron rich phases). Zr_(1-x)Y_(x)B₁₂ solid solutions contain the YB₆₆ phase, which in contrast to ScB₅₀, is not a β-rhombohedral boron doping phase, but a separate Y-B phase. YB₆₆ (Fm3c, FIG. 16) contains 1584 boron atoms and 24 Y atoms and is superhard (40.4±1.8 GPa at 0.49 N), potentially providing some extrinsic hardening for these samples.

For the Zr_(1-x)Sc_(x)B₁₂ solid solution, the hardness increases to 48.0±2.1 GPa at a composition of 50 at % Sc, compared to 40.4±1.8 GPa for pure ZrB₁₂ and 41.7±2.2 GPa for pure ScB₁₂. This hardness increase can again be attributed to a combination of intrinsic (solid solution hardening), since at this composition (Zr_(0.5)Sc_(0.5)B₁₂) ScB₁₂ is stabilized in the cubic structural type as well as extrinsic factors. The hardness of the solid solutions richer in Sc (x≥0.5) are harder than the corresponding samples richer in Zr (x≤0.5); this may be attributed to the fact that Zr_(1-x)Sc_(x)B₁₂ undergoes a cubic to tetragonal phase transition at 90-95 at. % Sc. This is similar to the martensitic transformation in steel, where the unit cell transforms from a cubic to a body-centered tetragonal lattice through a diffusionless transformation. Solid solutions richer in Sc also contain the ScB₅₀ phase (FIG. 16), which is a solid solution of Sc in f3-rhombohedral boron. This phase, like most metal boron doping phases, is superhard (H_(v)≥40 GPa) at 42.1±2.2 GPa at 0.49 N, providing some extrinsic hardening.

For the Y_(1-x)Sc_(x)B₁₂ solid solution, a hardness peak can be observed at 50 at. % Sc. The hardness increases to 45.2±2.1 GPa compared to 40.9±1.6 GPa for pure YB₁₂ and 41.7±2.2 GPa for pure ScB₁₂. Similarly to Zr_(1-x)Sc_(x)B₁₂, the hardness increase of Y_(1-x)Sc_(x)B₁₂ can be attributed to solid-solution hardnening as well as the presence of secondary boron rich phase, ScB₅₀ phase, which is superhard (H_(v)≥40 GPa at 0.5 N of applied loading). A cubic to tetragonal phase transition occurs at 90-95 at. % Sc for this solid solution.

In order to determine the cell parameters, Rietveld refinement was carried out using Maud software (Tables 1-3). For Zr_(1-x)Y_(x)B₁₂ the lattice parameter (a) of the cubic cell changed from 7.412 Å for pure ZrB₁₂ to 7.505 Å for pure YB₁₂ (FIGS. 1-3 and Table 1). The change and gradual increase of the cell parameters confirms that a solid solution has been formed. In order to check the composition of the Zr_(1-x)Y_(x)B₁₂ phase, EDS analysis was performed (Table 1). This analysis further confirmed the nearly perfect solid solution formation over all range of concentrations of Zr and Y in Zr_(1-x)Y_(x)B₁₂. As both of the parent dodecaborides (ZrB₁₂ and YB₁₂) are of the cubic-UB₁₂ (Fm3m) structural type, this system has no solid-state phase transformation.

For Zr_(1-x)Sc_(x)B₁₂ and Y_(1-x)Sc_(x)B₁₂ solid solutions, not only can a change in the lattice parameters be observed indicative of the formation of a solid solution (Tables 2-3), but a solid state phase transition between the cubic-UB₁₂ (Fm3m) and tetragonal-ScB₁₂ (I4/mmm) lattice types can be found as well. The phase transition occurs at ˜90-95 at. % Sc for Zr_(1-x)Sc_(x)B₁₂ and Y_(1-x)Sc_(x)B₁₂ solid solutions. A face-centered-cubic (FCC) to body-centered tetragonal (BCT) transition can be imagined if two FCC unit cells are positioned such that they share a face. Thus, the shared face-centered positions of the cubic cells become the body-centered positions of the tetragonal cell; the cubic a lattice parameter then becomes the tetragonal c lattice parameter, while the tetragonal a lattice parameter is composed of the cubic face diagonals and equals the cubic parameter a times

$\frac{\sqrt{2}}{2}.$

By refining the structural model to fit the data in the cubic and tetragonal unit cells over the whole range of solid solutions, we found that the values of the cubic a and tetragonal c lattice parameters stay essentially the same, within error, for low concentrations of scandium and diverges as they approach pure ScB₁₂. Therefore, at small concentrations of a secondary metal (5-10 at. %), one can speculate that the structure of the resulting mixed dodecaboride with scandium keeps the pure ScB₁₂ tetragonal unit cell, whereas with the addition of more secondary metal, the unit cell stabilizes into the cubic-UB₁₂ structure. To provide evidence for this speculation, a TEM image of showing the tetragonal diffraction pattern for Zr_(0.05)Sc_(0.95)B₁₂ can be seen in FIGS. 22-23.

Analyzing the crystal structure of ZrB₁₂ (ICSD 23861), YB₁₂ (ICSD 23860) and ScB₁₂ (ICSD 68028), one observes that tetragonal-ScB₁₂ has shorter metal-B bonds, while having longer B-B bonds than other cubic metal dodecaborides. This leads to not only a distortion of the cuboctahedron boron cages, but also to stronger metal-boron bonds in tetragonal-ScB₁₂. Addition of a secondary transition metal in ScB₁₂ allows for the alleviation of the cuboctahedral distortion and as a consequence stabilizes M_(1-x)Sc_(x)B₁₂ solid solution in the cubic structural type.

Metal dodecaboride samples exhibit interesting colors, ranging from violet for ZrB₁₂ to light blue for YB₁₂ and iceberg blue for ScB₁₂. The colors are a result of charge-transfer from the metal atoms to the network of boron cuboctahedron cages. FIG. 20 shows the colors of solid solution samples of the mixed metal dodecaborides taken using an optical microscope. The color change is most pronounced for the Zr_(1-x)Y_(x)B₁₂ solid solution, which goes from violet for ZrB₁₂ to light blue for YB₁₂. The color changes for Zr_(1-x)Sc_(x)B₁₂ and Y_(1-x)Sc_(x)B₁₂ are less pronounced due to the similarities of the shades of blue of YB₁₂ and ScB₁₂.

Analysing the thermal stability data from TGA for the hardest solid solutions of ZrB₁₂, YB₁₂ and ScB₁₂, one observes that the oxidation resistances for Zr_(0.5)Y_(0.5)B₁₂, Zr_(0.5)Sc_(0.5)B₁₂ and Y_(0.5)Sc_(0.5)B₁₂ are comparable to their parent compounds (FIG. 12). Whereas, the oxidation resistances for ZrB₁₂, YB₁₂ and ScB₁₂ are ˜610° C., ˜715° C. and ˜685° C., respectively, the mixed dodecaboride solid solutions are stable up until ˜630° C., ˜685° C. and ˜695° C., respectively. This high oxidation resistance suggests that dodecaborides could be a promising replacement for the current industrial standard, tungsten carbide, which oxidizes at ˜400° C. Furthermore, the densities for the hardest compositions are low, owing to their high boron content. X-ray densities of Zr_(0.5)Y_(0.5)B₁₂ (3.52 g/cm³), Zr_(0.5)Sc_(0.5)B₁₂ (3.32 g/cm³), and Y_(0.5)Sc_(0.5)B₁₂ (3.18 g/cm³) show that they are as light, if not lighter than diamond (3.52 g/cm³). The low density, superhardness and enhanced oxidation resistance makes metal dodecaborides an interesting choice as potential materials for cutting and machining or as lightweight protective coatings.

Zr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Pr_(x)B₁₂, and Zr_(1-x)Nd_(x)B₁₂

Pellets of Zr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Pr_(x)B₁₂, and Zr_(1-x)Nd_(x)B₁₂(x=0.05, 0.25, 0.50, 0.75 and 0.95) were prepared using high-purity metal and boron powders: amorphous boron (99+%, Strem Chemicals, USA), gadolinium (99%, Sigma-Aldrich, USA), zirconium (99.5%, Strem Chemicals, USA), samarium (Strem Chemicals, 99.9%), praseodymium (99.9%, Strem Chemicals, USA), and neodymium (99.8%, Strem Chemicals, USA). The metal to boron ratio was kept at a minimum of 1:20 to prevent the formation of lower borides (MB₆) as they are the ambient pressure most stable boride phases of Gd, Sm, Nd, and Pr. The weighed mixtures were homogenized in vials in a vortex mixer for ˜1 minute, then consolidated in a hydraulic press (Carver) under ˜10 tons before being arc melted (I>70 amps, T=1-2 min) under a high purity argon atmosphere.

The resultant pellets were broken into 2-4 pieces by gently tapping using a tool steel Plattner-style diamond crusher. Half of the pieces were crushed using the aforementioned tool steel Plattner-style diamond crusher to −325 mesh (≤45 μm) powder for powder XRD. PXRD was performed on a Bruker D8 Discover powder X-ray diffractometer (Bruker Corporation, Germany) utilizing a CuKα X-ray beam (λ=1.5418 Å) in the 5-100° 2 θ range with a scan speed of 0.1055°/s, time per step of 0.3 s. The phases analyzed were cross-referenced against the Joint Committee on Powder Diffraction Standards (JCPDS) database. Maud software was used to perform the unit cell refinements.

One piece was encapsulated in an epoxy/hardener set (Allied High Tech Products Inc., USA) to be polished to an optically flat finish on a semi-automated polisher (Southbay Technology Inc., USA) using both silicon carbide abrasive disks of 120-1200 grit (Allied High Tech Products Inc., USA) and 30-1 μm particle-size diamond films (Southbay Technology Inc., USA).

The polished samples were analyzed using an UltraDry EDS detector (Thermo Scientific, USA) attached to an FEI Nova 230 high-resolution scanning electron microscope (FEI Company, USA). Vickers hardness testing was performed using a MicroMet 2103 Vickers microhardness tester (Buehler Ltd., USA) with a pyramidal diamond indenter tip. 15 indents were made at applied loadings of 0.49, 0.98, 1.96 each, and a minimum of 10 indents were made at loadings of 2.94 and 4.9 N each, and were performed in random areas of the sample. A high resolution optical microscope (Zeiss Axiotech 100HD, Carl Zeiss Vision GmbH, Germany) with 500× magnification was used to measure the length of the diagonals of each indent. Vicker's hardness was calculated using the Equation below:

$H_{v} = \frac{1854.4F}{a^{2}}$

where F is the loading force applied in Newtons (N) and a is the average of the length of the two diagonals of each indent in micrometers.

Thermogravimetric analysis utilizing a Pyris Diamond TGA/DTA unit (TG-DTA, Perkin-Elmer Instruments, U.S.A.) was used to determine oxidation resistance. The profile used for heating and cooling in air was as follows: heat from 25 to 200° C. (at 20° C./min), hold at 200° C. for 30 minutes, heat from 200 to 1000° C. (at 2° C./min), hold at 1000° C. for₁₂₀ minutes, cool 1000 to 25° C. (at 5° C./min).

Phase determination and sample purity was determined using powder X-ray diffraction (PXRD) and energy-dispersive X-ray spectroscopy (EDS). PXRD data (2 Θ=5-100°) for Zr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Nd_(x)B₁₂ and Zr_(1-x)Pr_(x)B₁₂ solutions are shown in FIGS. 4-7. EDS data for Zr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Nd_(x)B₁₂ and Zr_(1-x)Pr_(x)B₁₂ (FIG. 18), hardness (FIG. 11) and thermogravimetric analysis (FIG. 13) data for Zr_(0.5)Gd_(0.5)B₁₂ are discussed in detail later in this section. Unit cell parameters and compositions for Zr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Nd_(x)B₁₂ and Zr_(1-x)Pr_(x)B₁₂ alloys are provided in Tables 4-7.

For Zr_(1-x)Gd_(x)B₁₂, the solubility limit of Gd in ZrB₁₂ is 54 at. % Gd, whereas for Zr_(1-x)Sm_(x)B₁₂, the solubility limit of Sm in ZrB₁₂ is ˜15 at. % Sm. For Zr_(1-x)Nd_(x)B₁₂, the solubility limit of Nd in ZrB₁₂ is ˜7 at. % Nd and for Zr_(1-x)Pr_(x)B₁₂, the solubility limit of Pr in ZrB₁₂ is 15 at. % Pr. The above solubilities were determined by powder XRD and EDS analyses. Past the solubility limit of Gd, Sm, Nd and Pr in ZrB₁₂, the amount of the respective hexaboride (MB₆) phases, which are the highest stable borides, increase (FIGS. 4-7). As metal dodecaborides are typically formed along the tie line of an incongruently melting phase, they are accompanied by a lower boride (MB₂ or MB₆) at metal to boron ratio of ˜1:12, and higher borides (MB₅₀ and MB₆₆) at larger metal to boron ratios 1:20. Cell parameters determined for each of the solid solution compositions as well as the metal composition for Zr_(1-x)Gd_(x)B₁₂ and Zr_(1-x)Sm_(x)B₁₂ are given in Tables 4-5. Note that the solubility of the secondary metal (Sm—Pr) in ZrB₁₂ decreases with increasing size of said metal, which is in good agreement with the size requirements for the metal dodecaboride formation as discussed above.

Vickers hardness testing from 0.49 N (low load) to 4.9 N (high load) was perfomed on samples of Zr_(1-x)Gd_(x)B₁₂ (x=0.05, 0.25 and 0.50) after the composition and purity of each was established. The hardness of Zr_(1-x)Gd_(x)B₁₂ solid solutions did not change (within the measurement error) remaining at around ˜40 GPa at 0.49 N, similar to the parent ZrB₁₂ (40.4±1.8 GPa).

Elemental maps and SEM images of selected samples of Zr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Nd_(x)B₁₂ and Zr_(1-x)Pr_(x)B₁₂ alloys (x=0.55, 0.30, 0.25 and 0.25 respectively) are presented in FIG. 18. For the Zr_(0.45)Gd_(0.55)B₁₂ solid solution, the presence of zirconium and gadolinium can be seen in the dodecaboride phase. The boron rich areas correspond to a higher boride phase GdB₆₆ (cubic, Fm3c structure, a=23.449 Å, ICSD 614306). The Zr_(0.70)Sm_(0.30)B₁₂ solid solution shows the presence of zirconium and samarium in the dodecaboride phase. Here, the samarium rich areas correspond to SmB₆ (cubic, Pm3m structure, a=4.133 Å, ICSD 194196), and the boron rich areas correspond to the higher boride phase SmB₆₆ (cubic, Fm3c structure, a=23.468 Å). The Zr_(0.75)Nd0.25B₁₂ and Zr_(0.75)Pr_(0.25)B₁₂ solid solutions show the presence of both zirconium and the secondary metals, neodymium and praseodymium, respectively, in the dodecaboride phase. The neodymium rich areas correspond to NdB₆ (cubic, Pm3m structure, a=4.127 Å, ICSD 614931), while the praseodymium rich areas correspond to PrB₆ (cubic, Pm3m structure, a=4.123 Å, ICSD 615183). In the samples containing Nd and Zr, the boron rich areas correspond to the higher boride phase NdB₆₆ (cubic, Fm3c structure, a=23.476 Å) and ZrBso (rhombohedral, R3m structure, a=10.932 Å, c=23.849 A), respectively. For praseodymium, however, the metal rich areas correspond to PrB₆ (cubic, Pm3m structure, a=4.123 Å, ICSD 615183), while the boron rich areas correspond to the higher boride phase ZrBso (rhombohedral, R3m structure, a=10.932 Å, c=23.849 Å) as the PrB₆₆ phase does not exist.

Maud software was used to perform the unit cell refinements. For Zr_(1-x)Gd_(x)B₁₂, the cubic unit cell parameter (a) reached a value of 7.453 Å for the alloy with 55 nominal at. % Gd, compared to 7.412 Å and 7.524 Å (value from high-pressure—6.5 GPa—synthesis) for pure ZrB₁₂ and GdB₁₂, respectively. The change in the unit cell suggests the formation of a solid solution between GdB₁₂ and ZrB₁₂. As more Gd is present in the alloy, the GdB₆ phase concentration increases, as it is the ambient pressure stable boride phase.

EDS analysis and calculations using Vegard's Law were used to determine the solubility limit of Gd in ZrB₁₂ (Table 4). Both methods gave a value 54 at. % Gd in ZrB₁₂; the excess Gd formed the boron rich GdB₆₆ and ZrB₅₀phase. For Zr_(1-x)Sm_(x)B₁₂, the cubic unit cell parameter (a) reached a value of 7.428 Å for the alloy with 30 nominal at. % Sm, compared to 7.412 Å for pure ZrB₁₂. As the high pressure synthesis of SmB₁₂ was not successful, since it likely requires a pressure in excess of 6.5 GPa, there is no literature value for its unit cell. However, using the composition from EDS analysis and unit cell refinements, the unit cell for pure SmB₁₂ can be determined through extrapolation 7.543 Å. Still, the change in the unit cell suggests the formation of a solid solution between SmB₁₂ and ZrB₁₂. As more Sm is present in the alloy, the SmB₆ phase concentration increases, as it is the ambient pressure stable boride phase for samarium.

For Zr_(1-x)Nd_(x)B₁₂ and Zr_(1-x)Pr_(x)B₁₂ there is a slight change in the unit cell parameter (a) compared to the pure ZrB₁₂, corresponding to the limited solubilities of Nd and Pr in ZrB₁₂, 7 and 4 at. %, respectively. Similar to SmB₁₂, the high-pressure synthesis of NdB₁₂ and PrB₁₂ was unsuccessful; therefore, it is not possible to compare the unit cells of the alloys with the unit cell of the pure compounds.

Another confimation of the solid solution formation of the dodecaboride phase can be directly observed using a light microscope (FIG. 21) going from pure ZrB₁₂ (violet) to Zr_(0.45)Gd_(0.55)B₁₂ (blue) and Zr_(0.70)Sm_(0.30)B₁₂ (blue-violet). The color change is due to the charge-transfer between the cuboctahedron boron cage network and the metal atoms. It also suggests that pure GdB₁₂ and SmB₁₂ should be blue, similar to YB₁₂, as Gd, Sm and Y are all in +3 oxidation states. The dark blue phase observed in Zr_(1-x)Sm_(x)B₁₂ is SmB₆.

The thermal stability of the zirconium-gadolinium and zirconium-samarium borides was measured in air using thermogravimetric analysis (FIG. 13). The Zr_(0.5)Gd_(0.5)B₁₂ sample is stable in air up to ˜630° C., while Zr_(0.75) SM0.25B₁₂ up to ˜620° C. compared to ˜610° C. for pure ZrB₁₂.

While preferred embodiments of the present disclosure have been shown and described herein, it will be obvious to those skilled in the art that such embodiments are provided by way of example only. Numerous variations, changes, and substitutions will now occur to those skilled in the art without departing from the disclosure. It should be understood that various alternatives to the embodiments of the disclosure described herein may be employed in practicing the disclosure. It is intended that the following claims define the scope of the disclosure and that methods and structures within the scope of these claims and their equivalents be covered thereby. 

What is claimed is:
 1. A composite matrix comprising: Zr_(1-x)M_(x)B₁₂, or Y_(1-x)Sc_(x)B₁₂; wherein: M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm), neodymium (Nd), or praseodymium (Pr); x is from 0.001 to 0.999.
 2. The composite matrix of claim 1, wherein the composite matrix is resistant to oxidation.
 3. The composite matrix of claim 1, wherein the composite matrix possesses a density of 4.0 g/cm³ or less.
 4. The composite matrix of claim 1, wherein the composite matrix possesses a hardness between 38.0 and 52.0 GPa.
 5. The composite matrix of claim 1, wherein the composite matrix is crystalline and comprises a unit cell that is cubic or tetragonal as determined by X-ray powder diffraction.
 6. The composite matrix of claim 5, wherein the unit cell is cubic and the length between two adjacent vertices in the unit cell is a, wherein a is from 7.350 to 7.550 Å.
 7. The composite matrix of claim 5, wherein the unit cell is tetragonal and comprises two distinct lengths between one vertex and at least two adjacent vertices, wherein the two distinct lengths comprise a first length c and a second length a, wherein c is from 7.350 to 7.550 Å and a is from 5.150 to 5.450 Å.
 8. The composite matrix of claim 1, wherein the composite matrix is Zr_(1-x)Y_(x)B₁₂.
 9. The composite matrix of claim 1, wherein the composite matrix is Zr_(1-x)Sc_(x)B₁₂.
 10. The composite matrix of claim 1, wherein the composite matrix is Y_(1-x)Sc_(x)B₁₂.
 11. The composite matrix of claim 1, wherein the composite matrix is Zr_(1-x)Gd_(x)B₁₂.
 12. The composite matrix of claim 1, wherein the composite matrix is Zr_(1-x)Sm_(x)B₁₂.
 13. The composite matrix of claim 1, wherein the composite matrix is Zr_(1-x)Nd_(x)B₁₂.
 14. The composite matrix of claim 1, wherein the composite matrix is Zr_(1-x)Pr_(x)B₁₂.
 15. A composite matrix comprising: A_(1-x)M_(x)B_(c); wherein: A is zirconium (Zr), yttrium (Y) or scandium (Sc); M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm), neodymium (Nd), praseodymium (Pr), terbium (Tb), dysprosium (Dy), holmium (Ho), erbium (Er), thulium (Tm), ytterbium (Yb), or lutetium (Lu); x is from 0.001 to 0.999; and c is 12-20; wherein if A is Zr and c is 12, M is not Y, Sc, Gd, Sm, Nd, or Pr; if A is Y and c is 12, M is not Sc; if A is Sc and c is 12, M is not Y; and A is not M.
 16. The composite matrix of claim 15, wherein the composite matrix is Y_(1-x)Gd_(x)B_(c), Sc_(1-x)Gd_(x)B_(c), Y_(1-x)Sm_(x)B_(c), Sc_(1-x)Sm_(x)B_(c), Y_(1-x)Nd_(x)B_(c), Sc_(1-x)Nd_(x)B_(c), Y_(1-x)Pr_(x)B_(c), Sc_(1-x)Pr_(x)B_(c), Zr_(1-x)Tb_(x)B_(c), Y_(1-x)Tb_(x)B_(c), Sc_(1-x)Tb_(x)B_(c), Zr_(1-x)Dy_(x)B_(c), Y_(1-x)Dy_(x)B_(c), Sc_(1-x)Dy_(x)B_(c), Zr_(1-x)Ho_(x)B_(c), Y_(1-x)Ho_(x)B_(c), Sc_(1-x)Ho_(x)B_(c), Zr_(1-x)Er_(x)B_(c), Y_(1-x)Er_(x)B_(c), Sc_(1-x)Er_(x)B_(c), Zr_(1-x)Tm_(x)B_(c), Y_(1-x)Tm_(x)B_(c), Sc_(1-x)Tm_(x)B_(c), Zr_(1-x)Yb_(x)B_(c), Y_(1-x)Yb_(x)B_(c), Sc_(1-x)Yb_(x)B_(c), Zr_(1-x)Lu_(x)B_(c), Y_(1-x)Lu_(x)B_(c), or Sci-XLuXB_(c).
 17. A method of preparing a composite matrix of claim 1, wherein any of Zr, Y, Sc, Gd, Sm, or Nd and B are homogenized in an agate mortar and pestle or a vortex mixer, pressed under an 8-12 ton load, and arc melted under an argon atmosphere.
 18. A method of preparing a composite matrix of claim 15, wherein any of Zr, Y, Sc, Gd, Sm, Nd, Pr, Tb, Dy, Ho, Er, Tm, Yb, or Lu and B are homogenized in an agate mortar and pestle or a vortex mixer, pressed under an 8-12 ton load, and arc melted under an argon atmosphere.
 19. A lightweight coating comprising the composite matrix of claim
 1. 20. A tool comprising a surface or body for cutting or abrading, wherein the surface or body comprises the composite matrix of claim
 1. 